
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
The Annual Interstellar Algebra Summit (AIAS) is held with a committee of four Martians, six Venusians, and five Earthlings. They sit at a round table with chairs numbered from $1$ to $15$ in clockwise order. AIAS rules mandate that a Martian must occupy chair number $1$, a Venusian must occupy chair number $7$, and an Earthling must occupy chair number $15$. Additionally, no Martian can sit immediately to the left of an Earthling, no Earthling can sit immediately to the left of a Venusian, and no Venusian can sit immediately to the left of a Martian. Determine the number of possible seating arrangements for this committee expressed as $N \cdot (4! \cdot 6! \cdot 5!)$. Find $N$.

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