
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 parametric equations of curve C: $$\begin{cases} x=a\cos\alpha \\ y=b\sin\alpha \end{cases}$$ (where $\alpha$ is the parameter), the point M $(1, \frac{\sqrt{2}}{2})$ on curve C corresponds to the parameter $\alpha= \frac{\pi}{4}$. Taking the origin O as the pole and the positive x-axis as the polar axis, we establish a polar coordinate system. The polar coordinates of point P are $(\sqrt{2}, \frac{\pi}{2})$. A line $l$ passes through point P and intersects curve C at two distinct points A and B. (1) Find the standard equation of curve C;  
(2) Find the range of values for $|PA|\cdot|PB|$.

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