
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 an ellipse $E: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a>b>0)$ with an eccentricity of $\frac{\sqrt{2}}{2}$ and upper vertex at B. Point P is on E, point D is at (0, -2b), and the maximum area of △PBD is $\frac{3\sqrt{2}}{2}$.
(I) Find the equation of E;
(II) If line DP intersects E at another point Q, and lines BP and BQ intersect the x-axis at points M and N, respectively, determine whether $|OM|\cdot|ON|$ is a constant value.

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