
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 Tri-Star System Mathematics Convention (TSMC) is attended by a committee of five Zetonians, five Pultonians, and five Earthlings. They are sitting around a round table with chairs numbered from $1$ to $15$ in clockwise order. According to convention rules, a Zetonian must occupy chair $1$, a Pultonian must occupy chair $15$, and furthermore, no Earthling can sit immediately to the left of a Zetonian, no Zetonian can sit immediately to the left of a Pultonian, and no Pultonian can sit immediately to the left of an Earthling. Determine the total number of possible seating arrangements for the committee if it can be expressed as $N \cdot (5!)^3$. Provide the value of $N$.

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