
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 a hyperbola C centered at the origin with an eccentricity of $\frac{2\sqrt{3}}{3}$ and one of its directrices given by the equation $x=\frac{3}{2}$,  
(1) Find the standard equation of the hyperbola C.  
(2) If a line $l$ given by $y=kx+\sqrt{2}$ has two distinct intersection points A and B with hyperbola C, and $\overrightarrow{OA} \cdot \overrightarrow{OB} > 2$ (where O is the origin), find the range of values for $k$.

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