
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 4x4 grid, four $\text{A's}$, four $\text{B's}$, four $\text{C's}$, and four $\text{D's}$ are placed so that each row and each column contains one of each letter, with two $\text{A's}$ in the upper left and lower right corners. Calculate the number of arrangements possible with the additional condition that no two adjacent cells (horizontally or vertically) contain the same letter.

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