
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 rectangular coordinate system $(xOy)$, the parametric equations of the curve $C$ are given by: $\begin{cases} x=a\cos \alpha, \\ y=b\sin \alpha, \end{cases} (\alpha \text{ is the parameter})$, and the parameter $\alpha = \frac{\pi }{4}$ corresponds to the point $M(1,\frac{\sqrt{2}}{2})$ on the curve $C$. Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive $x$-axis as the polar axis. The polar coordinates of point $P$ are $(\sqrt{2},\frac{\pi }{2})$, and line $l$ passes through point $P$ and intersects curve $C$ at two distinct points $A$ and $B$.

(I) Find the Cartesian equation of curve $C$;

(II) Find the range of values for $|PA|\cdot|PB|$.

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