
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 that 9 balls, numbered 1, 2, 3, 4, ..., 9, are to be placed into 9 boxes, also numbered 1, 2, 3, 4, ..., 9, with each box containing one ball, determine the total number of ways to do this such that exactly 4 balls do not match the numbers of their respective boxes.

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