
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
Let  $ S$  be the set of all positive integers whose all digits are  $ 1$  or  $ 2$ . Denote  $ T_{n}$  as the set of all integers which is divisible by  $ n$ , then find all positive integers  $ n$  such that  $ S\cap T_{n}$  is an infinite set.

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