
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
A futuristic human colony on Mars has established a governance system where there exists one Governor, 3 Deputy Governors, each having 3 Lieutenants. Each Lieutenant has 2 Subordinates. If the colony has 35 members, in how many ways can they choose the Governor, the Deputy Governors, the Lieutenants for each Deputy Governor, and the Subordinates under each Lieutenant?

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