
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 two different natural numbers whose arithmetic mean \( A \) and geometric mean \( G \) are both two-digit numbers, and where \( A \) and \( G \) can be transformed into each other by swapping the digits in either the units place or the tens place.

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