
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
Determine all pairs of *distinct* real numbers  $(x, y)$  such that both of the following are true:



- $x^{100} - y^{100} = 2^{99} (x-y)$
- $x^{200} - y^{200} = 2^{199} (x-y)$


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