
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
In the elective course 4-4: Coordinate System and Parametric Equations, the line described by the polar equation $\rho\cos\theta-\rho\sin\theta-1=0$ intersects the x-axis at point P, and intersects the ellipse described by the parametric equations $\begin{cases} x=2\cos\theta \\ y=\sin\theta \end{cases}$ (where $\theta$ is the parameter) at points A and B. Find the product $PA \cdot PB$.

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