
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
If  $a$  and  $b$  are nonzero real numbers such that  $\left| a \right| \ne \left| b \right|$ , compute the value of the expression
\[
  \left( \frac{b^2}{a^2} + \frac{a^2}{b^2} - 2 \right) \times
  \left( \frac{a + b}{b - a} + \frac{b - a}{a + b} \right) \times
  \left( 
    \frac{\frac{1}{a^2} + \frac{1}{b^2}}{\frac{1}{b^2} - \frac{1}{a^2}}
      - \frac{\frac{1}{b^2} - \frac{1}{a^2}}{\frac{1}{a^2} + \frac{1}{b^2}}
  \right).
\]

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