
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
Let  $ A$  be an integer not equal to  $ 0$ . Solve the following system of equations in  $ \mathbb{Z}^3$ .
 $ x \plus{} y^2 \plus{} z^3 \equal{} A$ 
 $ \frac {1}{x} \plus{} \frac {1}{y^2} \plus{} \frac {1}{z^3} \equal{} \frac {1}{A}$ 
 $ xy^2z^3 \equal{} A^2$ 

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