
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
Given the set $\{1,2,3,4,\dots,43,44,45\}$, two distinct numbers are selected such that the product of these two numbers equals the sum of the remaining 43 numbers in the set. Find the ratio of the larger number to the smaller number.

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