
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
In a $4 \times 4$ grid of 16 small squares, fill in 2 $a$'s and 2 $b$'s, with each square containing at most one letter. If the same letter is neither in the same row nor in the same column, how many different arrangements are there?

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