
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
In a math class, each dwarf needs to find a three-digit number without any zero digits, divisible by 3, such that when 297 is added to the number, the result is a number with the same digits in reverse order. What is the minimum number of dwarfs that must be in the class so that there are always at least two identical numbers among those found?

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