
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
Ten people are sitting around a circular table, each holding a fair coin. All ten people flip their coins, and those who flip heads stand while those who flip tails remain seated. Calculate the probability that no two adjacent people will stand.

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