
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 red hats, and 68 players are wearing green hats. A total of 132 players are paired into 66 teams of 2. If exactly 20 of these teams consist of players both wearing red hats, find the number of teams composed of players both wearing green hats.

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