
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In a number game between two very smart students A and B, a referee first writes the integers \(2, 3, \cdots, 2020\) on a blackboard, then deletes one of these numbers. Then A and B take turns deleting one number at a time (B deletes the first number, and then A deletes one). This continues until two numbers remain that are coprime (mutually prime). If the final two numbers are coprime, student A wins; otherwise, student B wins. According to these game rules, what is the probability that student A wins?

Present the answer in LaTex format: \boxed{Your answer}
user