
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 chess tournament, $64$ players are wearing green hats, and $68$ players are wearing red hats. There are $132$ players split into $66$ pairs for the first round. In exactly $25$ of these pairs, both players are wearing green hats. Calculate how many pairs have both players wearing red hats.
A) 25
B) 27
C) 32
D) 34
E) 36

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