
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
Find all integers \( k > 1 \) such that for some distinct positive integers \( a \) and \( b \), the number \( k^a + 1 \) can be obtained from \( k^b + 1 \) by reversing the order of its decimal digits.

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