
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
Clowns Pluh and Shmyak have six pairs of felt boots between them. Each pair of felt boots is painted in its own special color, and the boots in the pair are absolutely identical (not divided into left and right). In how many ways can both clowns simultaneously wear mismatched boots?

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