
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 moving point $E$ such that the product of the slopes of the lines from $E$ to points $A(2,0)$ and $B(-2,0)$ is $- \frac {1}{4}$, and the trajectory of point $E$ is curve $C$.  
$(1)$ Find the equation of curve $C$;  
$(2)$ Draw a line $l$ through point $D(1,0)$ that intersects curve $C$ at points $P$ and $Q$. Find the maximum value of $\overrightarrow{OP} \cdot \overrightarrow{OQ}$.

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