
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 numbers \( a \) and \( b \) satisfy the equation \( \frac{a^{2} b^{2}}{a^{4} - 2 b^{4}} = 1 \). Find all possible values of the expression \( \frac{a^{2} - b^{2}}{a^{2} + b^{2}} \).

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