
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 medieval society has a hierarchical system consisting of one king, 3 dukes (duke A, duke B, and duke C), each with 2 knights serving them. If this society has 12 members, what is the number of different ways to establish this hierarchy? Specifically, in how many ways can we choose the king, 3 dukes, and 2 knights for each duke?

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