
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
The line with the polar equation $\rho\cos \theta+\rho\sin \theta-1=0$ intersects the $x$-axis at point $P$ and intersects the ellipse defined by $\begin{cases} x=2\cos \theta, \\ y=\sin \theta \end{cases}$ (where $\theta$ is a parameter) at points $A$ and $B$. Find $|PA|\cdot|PB|$.

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