
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 five teacups and five lids, each numbered from 1 to 5. When covering the teacups with the lids, determine the number of ways to have at least two lids match the numbers of their respective teacups.

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