
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
Members of the mathematical circle "Seeker" noticed that the number 289 can be obtained by squaring the sum of the digits 8 and 9, i.e., \( 289 = (8 + 9)^{2} \). They decided to find such three-digit numbers with a hundreds digit less than four, each of which equals the sum of its tens and units digits raised to the power of the hundreds digit. Help them solve this problem.

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