
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
The non-zero real numbers \(a\) and \(b\) satisfy the equation

$$
\frac{a^{2} b^{2}}{a^{4}-2 b^{4}}=1
$$

Find, with reasoning, all the values taken by the expression

$$
\frac{a^{2}-b^{2}}{a^{2}+b^{2}}
$$

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