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

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