
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 consists of 12 players, including two pairs of twins, Alex and Brian, and Chloe and Diana. In how many ways can we choose a team of 5 players if no pair of twins can both be in the team lineup simultaneously?

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