
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 five balls, numbered 1 through 5, and five boxes, also numbered 1 through 5, with one ball per box, determine the number of ways to arrange the balls such that exactly two balls have the same number as the boxes they are in.

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