
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 letters "a" and 2 letters "b" in a $4 \times 4$ grid with 16 small squares, with at most 1 letter in each small square, ensuring that no identical letters are in the same row or column. How many different ways can this be done? (Use numbers to answer).

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