
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 \(a\) and \(b\) be positive real numbers such that \(a^4 + b^4 = a + b\). Given that \(a^2 + b^2 = 2\), simplify
\[
\frac{a^2}{b^2} + \frac{b^2}{a^2} - \frac{1}{a^2b^2}.
\]

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