
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 \(x\), \(y\), and \(z\) be nonzero real numbers such that \(x + y + z = 3\). Simplify
\[
\frac{1}{y^2 + z^2 - x^2} + \frac{1}{x^2 + z^2 - y^2} + \frac{1}{x^2 + y^2 - z^2}.
\]

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