
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 $E$: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ passing through the point $(0, \sqrt{2})$, with an eccentricity of $\frac{\sqrt{6}}{3}$, and point $O$ as the coordinate origin.

(1) Find the standard equation of the ellipse $E$;

(2) Draw a line $l$ passing through the left focus $F$ of the ellipse, intersecting the ellipse at points $P$ and $Q$. Determine the range of values for $\overrightarrow{OP} \cdot \overrightarrow{OQ}$.

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