
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
To celebrate the  $20$ th LMT, the LHSMath Team bakes a cake. Each of the  $n$  bakers places  $20$  candles on the cake. When they count, they realize that there are  $(n -1)!$  total candles on the cake. Find  $n$ .

*Proposed by Christopher Cheng*

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