
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
The Howlers, coached by Coach Loudvoice, have 15 players. Three players, named Al, Ben, and Cara, refuse to play together. Coach Loudvoice needs to form starting lineups consisting of 6 players. How many starting lineups can Coach Loudvoice make, if the starting lineup cannot contain all three of Al, Ben, and Cara together?
(Note: The order of the 6 players in the lineup does not matter; lineups are considered the same if they consist of the same 6 players.)

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