
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 all letters are neither in the same row nor in the same column, then the total number of different ways to fill them is

              (use numbers to answer).

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