
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
Among all permutations of the numbers 1, 2, 3, 4, 5, 6, 7, find the total number of distinct permutations such that any two adjacent numbers are coprime.

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