
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 from $1$ to $5$ and five boxes also numbered from $1$ to $5$, calculate the total number of arrangements such that each box contains exactly one ball and exactly two balls have the same numbers as their boxes.

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