
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
Place 2 'a's and 2 'b's into the 16 squares shown in the diagram, with at most one letter per square. If the same letters are neither in the same row nor in the same column, the total number of different filling methods is $\boxed{3960}$.

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