
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
Calculate the number of ways to place 10 balls labeled with the numbers 1 to 10 into 10 boxes also labeled with the numbers 1 to 10, such that each box contains one ball, and exactly 3 balls are placed in boxes with non-matching labels.

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