
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
Given that $\text{A}$ is placed in the upper left corner and $\text{B}$ is placed in the middle of the first column, determine the number of possible arrangements of three $\text{A's}$, three $\text{B's}$, and three $\text{C's}$ in a 3x3 grid.

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