
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
For any given real  $a, b, c$  solve the following system of equations:  $$ \left\{\begin{array}{l}ax^3+by=cz^5,az^3+bx=cy^5,ay^3+bz=cx^5.\end{array}\right. $$  *Proposed by Oleksiy Masalitin, Bogdan Rublov*

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