
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
Solve the following system of equations in real numbers:  $$ \left\{\begin{array}{l}x^2=y^2+z^2,x^{2024}=y^{2024}+z^{2024},x^{2025}=y^{2025}+z^{2025}.\end{array}\right. $$  *Proposed by Mykhailo Shtandenko, Anton Trygub, Bogdan Rublov*

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