
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 ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ passes through point $M(\sqrt{6},1)$, and its eccentricity is $\frac{\sqrt{2}}{2}$.
(I) Find the standard equation of the ellipse;
(II) Given point $P(\sqrt{6},0)$, if $A$ and $B$ are two moving points on the known ellipse, and satisfy $\overrightarrow{PA} \cdot \overrightarrow{PB}=-2$, determine whether line $AB$ always passes through a fixed point. If it does, provide a proof and find the coordinates of the fixed point; if not, explain the reason.

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