
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
Two non-zero numbers are given. If each of them is increased by one, their product doubles. By how many times will their product increase if each of the original numbers is squared and then decreased by one?

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