
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
A value of $x$ satisfying the equation $x^2 + c^2 = (a - x)^3$ is?
A) $\frac{c^2 - a^3}{3a^2 - 1}$
B) $\frac{a^3 - c^2}{3a^2 + 1}$
C) $\frac{c^2 + a^3}{3a^2 - 1}$
D) $\frac{a^3 + c^2}{3a^2 + 1}$

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