
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 Interplanetary Mathematics Examination (AIME) committee meeting involves a setup where seven Martians, five Venusians, and eight Earthlings sit around a round table with chairs numbered from $1$ to $20$. The seating rules require that a Martian must occupy chair $1$ and an Earthling must occupy chair $20$. Additionally, no Earthling can sit immediately to the left of a Martian, no Martian can sit immediately to the left of a Venusian, and no Venusian can sit immediately to the left of an Earthling. Calculate the number of possible seating arrangements if the number of arrangements is given by $N \cdot (7! \cdot 5! \cdot 8!)$. Find $N$.

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