
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 two nonzero numbers, if 1 is added to each of them, and 1 is subtracted from each of them, the sum of the reciprocals of the four resulting numbers will be 0. What number can be obtained if the sum of the original numbers is subtracted from the sum of their reciprocals? Find all possibilities.

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