
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, coached by Coach Loudvoice, have 15 players, but three of them, Ben, Tom, and Dan, refuse to play together. Additionally, one player, Alex, is injured and cannot participate. How many starting lineups (of 5 players) can Coach Loudvoice make if the starting lineup cannot contain more than one among Ben, Tom, and Dan, and cannot include Alex at all?

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