
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 10 balls numbered 1, 2, ..., 10 into 10 boxes also numbered 1, 2, ..., 10, with each box containing one ball. Find the number of ways to place the balls such that exactly 3 balls do not match the numbers of their boxes.

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