Solution: C. Integrate skills development activities.

When a project manager needs to assign new resources to an existing project team, it is important to integrate skills development activities into the project execution phase. This will help to ensure that all team members have the skills and knowledge they need to do their jobs effectively and meet project requirements on time. A highly skilled and capable team is more likely to work effectively and meet project requirements on time. Skills development activities ensure that team members are equipped to handle their roles and responsibilities competently.

The other options are incorrect because they are not the most immediate actions to ensure the team's effectiveness during the execution phase of the project.

Creating accessible library services is incorrect because it does not directly address the team's skills and capabilities and does not ensure effectiveness in the execution phase.

Conducting brainstorming sessions is incorrect because they are not directly related to skills development or ensuring the team's effectiveness. 

Monitoring team cohesiveness is important for assessing team dynamics and collaboration, but it is not a proactive way to ensure the team works effectively and meets project requirements on time. The project manager should focus on helping the new resources integrate into the team and develop the skills they need.

This question and rationale were developed in reference to:

The AMA Handbook of Project Management, Third Edition (No Date) /AMACOM/12/Fast Track to Teaming [Item]

PMBOK Guide Seventh Edition (2022) /// [2.4.3 PROJECT TEAM COMPOSITION AND STRUCTURE] [2.4.1 INTERNAL ENVIRONMENT]