
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

Pete wrote on the board \( n \) consecutive two-digit octal numbers (\( n \geqslant 2 \)) forming an arithmetic progression with a common difference of 8, where the first number does not contain the digit 2. Vasya thought this was the octal representation of a natural number \( x \) and factored \( x \) into prime factors. It turned out that there were exactly two factors, and they differed by 2. What is written on the board?

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