
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
When Kolya's classmates asked for the number of his family's apartment in the new house, Kolya, a math enthusiast, answered: "The number of our apartment is a three-digit number that is a perfect cube. If you swap the hundreds and units digits, you get a prime number." What is Kolya's apartment number?

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