
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
The natural number obtained by reversing the digits of a given natural number is called the reverse number of the original number. For example, the reverse number of the five-digit number 13245 is 54231, and the reverse number of 11722 is 22711. If the reverse number of a five-digit number \( n \) is a multiple of 4, what is the smallest such \( n \) and what is the largest such \( n \)?

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