
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
Petya writes different three-digit natural numbers on the board, each of which is divisible by 3, and the first two digits differ by 2. What is the maximum number of such numbers he can write down if they end in 6 or 7?

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