
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
Three tired cowboys entered a saloon and hung their hats on a bison horn at the entrance. Late at night, when the cowboys were leaving, they were unable to distinguish one hat from another and randomly took three hats. Find the probability that none of them took their own hat.

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