
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
Arrange the letters a, a, b, b, c, c into three rows and two columns, with the requirement that each row has different letters and each column also has different letters, and find the total number of different arrangements.

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