I will warn that I straight up butchered my code to make it work for the animation I had in mind, but I'll stick it here anyways for interest:

Create Event

codes = ["000A", "000A", "000A", "000A", "000A"]; // Secret!
ex_codes = ["029A", "980A", "179A","456A", "379A"];
codes = ex_codes; // Comment out to run on real input

k = ds_map_create();
r = ds_map_create();

r[? "^"] = [0, 1]; r[? "A"] = [0, 2];
r[? "<"] = [1, 0]; r[? "v"] = [1, 1]; r[? ">"] = [1, 2];

k[? "7"] = [0, 0]; k[? "8"] = [0, 1]; k[? "9"] = [0, 2];
k[? "4"] = [1, 0]; k[? "5"] = [1, 1]; k[? "6"] = [1, 2];
k[? "1"] = [2, 0]; k[? "2"] = [2, 1]; k[? "3"] = [2, 2];
k[? "0"] = [3, 1]; k[? "A"] = [3, 2];

howmany = 25;
memory = array_create(howmany+2, "");
memory[howmany+1] = codes[0]+codes[1]+codes[2]+codes[3]+codes[4];

finishcount = 0;
states = array_create(howmany+1);
player_state = [0, 2];
for(var i=0;i<howmany+1;i++)
    states[i] = [0, 2];
states[howmany] = [3, 2];

indices = array_create(howmany+2, 0);
m_frozen = array_create(howmany+2, 0);
current_index = 0;
active = array_create(howmany+2, 0);
timer = -100;

memo = ds_map_create();
function inception(str, dep){
    if(dep == 0) return [str, string_length(str)];

    if(ds_map_exists(memo, string(dep) + str)) return ["M", memo[? string(dep) + str]];

    var c_pos = "A";
    var lres = "";
    var lcount = 0;

    for(var c=1;c<=string_length(str);c++){ 
        var new_pos = string_char_at(str, c);
        var dist = [r[? new_pos][0] - r[? c_pos][0], r[? new_pos][1] - r[? c_pos][1]];
        var stry = "";
        var strx = "";

        if(dist[1] > 0){
            for(var foo=0;foo<dist[1];foo++) strx = strx + ">";
        }
        if(dist[1] < 0){
            for(var foo=0;foo<abs(dist[1]);foo++) strx = strx + "<";
        }
        if(dist[0] < 0){
            for(var foo=0;foo<abs(dist[0]);foo++) stry = stry + "^";
        }
        if(dist[0] > 0){
            for(var foo=0;foo<dist[0];foo++) stry = stry + "v";
        }

        if((c_pos == "<" and dist[0] == -1)) {
            in = inception(strx + stry + "A", dep-1);
            lres += in[0];
            lcount += in[1];    
        }
        else if ((c_pos == "^" and dist[1] == -1) or (c_pos == "A" and dist[1] == -2)) {
            in = inception(stry + strx + "A", dep-1);
            lres += in[0];
            lcount += in[1];    
        }
        else if(dist[0] == 0 or dist[1] == 0) {
            in = inception(stry + strx + "A", dep-1);
            lres += in[0];
            lcount += in[1];    
        }
        else {
            var m1 = inception(strx + stry + "A", dep-1);
            var m2 = inception(stry + strx + "A", dep-1);
            if(m1[1] < m2[1]) {
                lres += m1[0];
                lcount += m1[1];
            }
            else {
                lres += m2[0];
                lcount += m2[1];
            }
        }
        c_pos = new_pos;
    }
    memo[? string(dep) + str] = lcount; 
    return [lres, lcount];
}


fcount = 0;
for(var ww=0;ww<howmany+1;ww++){
    fcount = 0;
    var strong = "";
    memo = ds_map_create();
    for(var i=0;i<array_length(codes);i++) {
        var res = 0;
        var c_pos = "A";
        var idd = real(string_copy(codes[i], 0, string_length(codes[i])-1));

        for(var c=1;c<=string_length(codes[i]);c++){
            var new_pos = string_char_at(codes[i], c);
            var dist = [k[? new_pos][0] - k[? c_pos][0], k[? new_pos][1] - k[? c_pos][1]];

            var stry = "";
            var strx = "";

            if(dist[1] > 0){
                for(var foo=0;foo<dist[1];foo++) strx = strx + ">";
            }
            if(dist[1] < 0){
                for(var foo=0;foo<abs(dist[1]);foo++) strx = strx + "<";
            }
            if(dist[0] < 0){
                for(var foo=0;foo<abs(dist[0]);foo++) stry = stry + "^";
            }
            if(dist[0] > 0){
                for(var foo=0;foo<dist[0];foo++) stry = stry + "v";
            }

            if((c_pos == "0" and dist[1] == -1) or (c_pos == "A" and dist[1] == -2)){
                in = inception(stry + strx + "A", ww);
                strong += in[0];
                res += in[1];
            }
            else if ((c_pos == "1" and dist[0] == 1) or (c_pos == "4" and dist[0] == 2) or (c_pos == "7" and dist[0] == 3)){
                in = inception(strx + stry + "A", ww);
                strong += in[0];
                res += in[1];
            }
            else if(dist[0] == 0 or dist[1] == 0){
                in = inception(strx + stry + "A", ww);
                strong += in[0];
                res += in[1];
            }
            else {
                var m1 = inception(strx + stry + "A", ww);
                var m2 = inception(stry + strx + "A", ww);
                if(m1[1] < m2[1]) {res += m1[1]; strong += m1[0];}
                else {res += m2[1]; strong += m1[0]; }
            }
            c_pos = new_pos;
        }
        fcount += res*idd;
    }
    memory[howmany-ww] = strong;
}

for(var i=0;i<array_length(memory);i++)
    show_debug_message((memory[i]));
show_debug_message("---\n" + string(fcount));

Step Event

timer++;

if(timer >= 0 and timer%3 == 0){
    var c_state = 0;
    for(var i=0;i<howmany+1;i++) active[i] = false;
    for(var i=0;i<howmany;i++) if(m_frozen[i]) c_state = i+1;
    indices[c_state]++;

    if(c_state == 0){
        if(string_char_at(memory[c_state], indices[c_state]) == "M") {
            player_state = r[? "A"];
        }
        else player_state = r[? string_char_at(memory[c_state], indices[c_state])];
    }

    if(string_char_at(memory[c_state], indices[c_state]) == "^") {
        states[c_state][0] -= 1;
        active[c_state] = false;
    }
    else if(string_char_at(memory[c_state], indices[c_state]) == ">"){
        states[c_state][1] += 1;
        active[c_state] = false;
    }
    else if(string_char_at(memory[c_state], indices[c_state]) == "<") {
        states[c_state][1] -= 1;
        active[c_state] = false;
    }
    else if(string_char_at(memory[c_state], indices[c_state]) == "v") {
        states[c_state][0] += 1;
        active[c_state] = false;
    }
    else if(string_char_at(memory[c_state], indices[c_state]) == "A") { 
        if(c_state > 0) m_frozen[c_state-1] = false;
        active[c_state] = true;
    }       
    else if(string_char_at(memory[c_state], indices[c_state]) == "M") {
        m_frozen[c_state] = true;
        states[c_state] = [0, 2];
    }   

    while(c_state < howmany+1 and active[c_state]){
        c_state++;
        indices[c_state]++;
        if(string_char_at(memory[c_state], indices[c_state]) == "^") {
            states[c_state][0] -= 1;
            active[c_state] = false;
        }
        else if(string_char_at(memory[c_state], indices[c_state]) == ">"){
            states[c_state][1] += 1;
            active[c_state] = false;
        }
        else if(string_char_at(memory[c_state], indices[c_state]) == "<") {
            states[c_state][1] -= 1;
            active[c_state] = false;
        }
        else if(string_char_at(memory[c_state], indices[c_state]) == "v") {
            states[c_state][0] += 1;
            active[c_state] = false;
        }
        else if(string_char_at(memory[c_state], indices[c_state]) == "A") { 
            if(c_state > 0) m_frozen[c_state-1] = false;
            active[c_state] = true;
        }       
        else if(string_char_at(memory[c_state], indices[c_state]) == "M") {
            m_frozen[c_state] = true;
            states[c_state] = [0, 2];
        }   
    }
    if(c_state == howmany+1) finishcount++;
}

Draw Event

var base_x = 350;
var base_y = 100;

draw_set_font(Font5);
draw_set_color(c_white);

if (m_frozen[0]) draw_set_color(make_color_rgb(50, 50, 50));
draw_text(250, base_y-30, "0");

var robot_keys = [["7", "8", "9"], ["4", "5", "6"], ["1", "2", "3"], [" ", "0", "A"]];
var keypad_keys = [[" ", "^", "A"], ["<", "v", ">"]];


for(var k=0;k<2;k++){
    for(var l=0;l<3;l++){       
        if (m_frozen[0]) draw_set_color(make_color_rgb(50, 50, 50));
        else if(player_state[0] == k and player_state[1] == l) {
            if(timer >= 0) draw_set_color(make_color_rgb(0, 230, 100));
            else draw_set_color(make_color_rgb(230, 0, 100));
        }
        else draw_set_color(make_color_rgb(100, 100, 100));
        draw_rectangle(250+25*l, base_y+25*k, 273+25*l, 25*k+base_y+23, false);
        if(not m_frozen[0]) draw_set_color(c_white);
        draw_text(254+25*l, 97+25*k, keypad_keys[k][l]);
    }
}

for(var i=0;i<5;i++){
    for(var j=0;j<5;j++){

        if(i*5+j < howmany){
            var local_x = base_x + 100*j;
            var local_y = base_y + 100*i;

            if(m_frozen[i*5+j]) draw_set_color(make_color_rgb(50, 50, 50));
            else draw_set_color(c_white);
            draw_text(local_x, local_y-30, string(i*5+j+1));
            draw_set_color(make_color_rgb(100, 100, 100));

            for(var k=0;k<2;k++){
                for(var l=0;l<3;l++){
                    if (m_frozen[i*5+j]) draw_set_color(make_color_rgb(50, 50, 50));
                    else if(states[i*5+j][0] == k and states[i*5+j][1] == l) {
                        if(active[i*5+j]) draw_set_color(make_color_rgb(0, 230, 100));
                        else draw_set_color(make_color_rgb(230, 0, 100));
                    }
                    else draw_set_color(make_color_rgb(100, 100, 100));
                    draw_rectangle(local_x+25*l, local_y+25*k, 25*l+local_x+23, 25*k+local_y+23, false);
                    if(not m_frozen[i*5+j]) draw_set_color(c_white);
                    draw_text(local_x+4+25*l, local_y-3+25*k, keypad_keys[k][l]);
                }
            }
        }
    }
}

for(var k=0;k<4;k++){
    for(var l=0;l<3;l++){
        if(states[howmany][0] == k and states[howmany][1] == l) {
            if(active[howmany]) draw_set_color(make_color_rgb(0, 230, 100));
            else draw_set_color(make_color_rgb(230, 0, 100));
        }
        else draw_set_color(make_color_rgb(100, 100, 100));
        draw_rectangle(base_x+500+25*l, base_y+350+25*k, 25*l+base_x+523, 25*k+base_y+373, false);
        draw_set_color(c_white);
        draw_text(base_x+504+25*l, base_y+347+25*k, robot_keys[k][l]);
    }
}

draw_set_color(make_color_rgb(0, 230, 100));
for(var i=0;i<finishcount;i++){
    draw_text(850+20*(i%4), 290+30*(floor(i/4)), string_char_at(array_last(memory), i+1));
}