
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
There are six teacups and six teacup lids, each numbered from 1 to 6. If these six lids are to be placed on the teacups such that exactly two of the lids match the teacup numbers, calculate the total number of ways this can be done.

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