
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
You have $7$ red shirts, $6$ green shirts, $7$ blue shirts, $8$ pairs of pants (which include $3$ blue pairs), $10$ red hats, $9$ green hats, and $4$ blue hats. How many outfits can you create where the shirt and hat cannot have the same color, and the pants and the hat must also not match in color?

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