
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
Given the curve $\frac{x^{2}}{a} - \frac{y^{2}}{b} = 1$ and the line $x + y - 1 = 0$ intersect at points $P$ and $Q$, with $\overrightarrow{OP} \cdot \overrightarrow{OQ} = 0$ ($O$ is the origin), determine the value of $\frac{1}{a} - \frac{1}{b}$.

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