
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 \(a, b,\) and \(c\) be three distinct numbers. Solve the system

$$
\left\{\begin{aligned}
z + ay + a^{2}x + a^{3} &= 0 \\
z + by + b^{2}x + b^{3} &= 0 \\
z + cy + c^{2}x + c^{3} &= 0
\end{aligned}\right.
$$

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