
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
A positive integer  $n$  is called *smooth* if there exist integers  $a_1,a_2,\dotsc,a_n$  satisfying
\[a_1+a_2+\dotsc+a_n=a_1 \cdot a_2 \cdot \dotsc \cdot a_n=n.\]
Find all smooth numbers.

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