
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
Fill 2 $a$'s and 2 $b$'s into the 16 squares as shown in the diagram, with each square containing at most one letter. If the same letters cannot be in the same row or column, how many different ways can this be done? (Answer with a number.)

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