
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
In a given mathematical relationship, $wx = a^2, wy=b^2,$ and $wz = c^2$, solve for the sum $x^2+y^2+z^2$. Given that none of the quantities $w$, $x$, $y$, $z$, $a$, $b$, or $c$ is zero.
A) $\frac{a^3 + b^3 + c^3}{w^2}$
B) $\frac{a^2b^2 + b^2c^2 + c^2a^2}{w^2}$
C) $\frac{a^4 + b^4 + c^4}{w^2}$
D) $\frac{a^2+b^2+c^2}{w^2}$
E) $\frac{a^2+b^2+c^2}{w}$

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