
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
If
\[
a\left(\frac{x}{c}\right) + b\left(\frac{y}{a}\right) + c\left(\frac{z}{b}\right) = 5 \quad \text{and} \quad \frac{c}{x} + \frac{a}{y} + \frac{b}{z} = 0,
\]
find \( \frac{x^2}{c^2} + \frac{y^2}{a^2} + \frac{z^2}{b^2}. \)

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