
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
A basketball team has 15 players including 2 captains. In a free throw contest, each captain competes to see who can score the most free throws. For each captain, every other player on the team, including the other captain, takes turns making free throws.

How many free throws must be taken to ensure that each player has attempted free throws against each of the captains?

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