
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 $x,$ $y,$ $z$ be real numbers such that $0 \leq x,$ $y,$ $z \leq 1.$ Find the minimum value of
\[
\frac{1}{(1 - x^2)(1 - y^2)(1 - z^2)} + \frac{1}{(1 + x^2)(1 + y^2)(1 + z^2)}.
\]

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