
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 Dunkers are coached by Coach Loudvoice. The Dunkers have 15 players, but three of them, Tom, Dick, and Harry, refuse to play together in any combination of two or more. How many starting lineups (of 5 players) can Coach Loudvoice make, if the starting lineup can't contain any two of Tom, Dick, and Harry together?

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