
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
Given a round dining table with seats named _A_, _B_, _C_, _D_, _E_, _F_ and six people (three adults and three children) to be seated, calculate the total number of different seating arrangements such that no two children sit next to each other.

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