
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
Replace the larger of two distinct natural numbers with their difference. Continue this operation until the two numbers are the same. For example, for the pair (20, 26), the process is as follows:
\[ (20, 26) \rightarrow (20, 6) \rightarrow (14, 6) \rightarrow (8, 6) \rightarrow (2, 6) \rightarrow (2, 4) \rightarrow (2, 2) \]

1. Perform the above operation on the pair (45, 80).
2. If the operation is performed on two four-digit numbers and the final same number obtained is 17, find the maximum possible sum of these two four-digit numbers.

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