
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 $a,$ $b,$ $c,$ and $d$ be nonzero real numbers such that $a + b + c + d = 0.$ Simplify
\[
\frac{1}{b^2 + c^2 + d^2 - a^2} + \frac{1}{a^2 + c^2 + d^2 - b^2} + \frac{1}{a^2 + b^2 + d^2 - c^2} + \frac{1}{a^2 + b^2 + c^2 - d^2}.
\]

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