
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
Suppose there are six teacups numbered 1, 2, 3, 4, 5, 6, and six teacup lids also numbered 1, 2, 3, 4, 5, 6. If these six lids are to be placed on the teacups such that exactly 2 lids match the numbers of their respective teacups, find the total number of ways to do this.

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