
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
 $12$  people stand in a row. Each person is given a red shirt or a blue shirt. Every minute, exactly one pair of two people with the same color currently standing next to each other in the row leave. After  $6$  minutes, everyone has left. How many ways could the shirts have been assigned initially?

*Proposed by Evan Chang*

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