
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
Tac is dressing his cat and has four indistinguishable socks, four indistinguishable shoes, and four indistinguishable snow-shoes. Tac randomly selects pieces of clothing and places them on random legs of his cat, ensuring no more than one of each type of clothing is placed on any leg. What is the probability that, at the end, each snow-shoe on any leg is correctly placed on top of a shoe, which is on top of a sock?

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