
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
Fox Alice thought of a two-digit number and told Pinocchio that this number is divisible by $2, 3, 4, 5,$ and $6$. However, Pinocchio found out that exactly two of these five statements are actually false. What numbers could Fox Alice have thought of? Indicate the number of possible options in the answer.

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