
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
In a special session of the Interplanetary Mathematics Examination Board, a committee consists of six Martians, six Venusians, and six Earthlings. They sit at a round table with chairs numbered from $1$ to $18$ in a clockwise direction. As per the committee rules, chair $1$ must be occupied by a Martian, and chair $18$ by an Earthling. Additionally, a Martian cannot sit immediately to the left of a Venusian, a Venusian cannot sit immediately to the left of an Earthling, and an Earthling cannot sit immediately to the left of a Martian. The number of possible seating arrangements for the committee is $N \cdot (6!)^3$. Determine $N$.

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