
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
Polina thought of a natural number. Her friends asked the following questions:

Masha: Is it divisible by 11?

Irina: Is it divisible by 13?

Anya: Is it less than 15?

Olya: Is it divisible by 143?

Polina responded affirmatively to only two out of the four questions. What numbers could Polina have thought of? Provide all possible options.

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