
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

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

Alyona: Is it divisible by 7?

Lena: Is it divisible by 5?

Rita: Is it less than 9?

Sveta: Is it divisible by 35?

Katya answered affirmatively to only two out of the four questions. What numbers could Katya have thought of? List all possible options.

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