
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 Interstellar Mathematics Summit (IMS) is organized by a committee of four Martians, four Venusians, and four Earthlings. They sit at a round table with chairs numbered from $1$ to $12$ in clockwise order. According to the summit rules, a Martian must occupy chair $1$ and a Venusian must occupy chair $12$. Furthermore, 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. The number of possible seating arrangements for the committee is $K \cdot (4!)^3$. Find $K$.

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