
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, Tim, Mike, and Sam, refuse to play together. How many starting lineups (of 5 players) can Coach Loudvoice make, if the starting lineup can't contain all three of Tim, Mike, and Sam together?

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