
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
Given a centipede with ten legs, one sock, and one shoe for each leg, determine the number of different orders in which the centipede can put on its socks and shoes, given that, on each leg, the sock must be put on before the shoe.

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