
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 different balls - red, black, blue, and yellow - into three different boxes, with at least one ball in each box. The red and blue balls cannot be in the same box. How many different arrangements are there?

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