
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
There is a natural number written on the board. Five students made the following statements about this number:

- Petya: "This number is greater than 10."
- Kolya: "This number is at least 11."
- Vasya: "This number is greater than 12."
- Dima: "This number is less than 12."
- Oleg: "This number is at most 12."

Find the maximum possible number of correct statements.

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