
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 $M: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ with an eccentricity of $\frac{\sqrt{2}}{2}$, and its upper vertex $B$ is the focus of the parabola $x^{2}=4y$.
(I) Find the standard equation of the ellipse $M$;
(II) If $P$, $Q$ are two moving points on the ellipse $M$, and $OP \perp OQ (O$ is the origin of the coordinate$)$, draw $OR \perp PQ$ at $R$, find the trajectory equation of point $R$.

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