
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 four identical white balls and five identical black balls into three different boxes, such that each box contains both white and black balls, and each box contains at least two balls. Calculate the total number of different arrangements.

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