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

Luda: Is it divisible by 7?
Natasha: Is it divisible by 11?
Marina: Is it less than 13?
Irina: Is it divisible by 77?

Galina answered "yes" to exactly two out of the four questions. What possible numbers could Galina have thought of? List all possible options.

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