
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
The teacher wrote a two-digit number on the board. Each of the three boys made two statements.

- Andrey: "This number ends in the digit 6" and "This number is divisible by 7."
- Borya: "This number is greater than 26" and "This number ends in the digit 8."
- Sasha: "This number is divisible by 13" and "This number is less than 27."

It is known that each of the boys told the truth once and made a mistake once. What number could have been written on the board? List all possible options.

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