
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 that $A(-2,0)$ is the left vertex of the ellipse $C: \frac{{x}^{2}}{{a}^{2}} + \frac{{y}^{2}}{{b}^{2}} = 1 (a > b > 0)$, the line $l$ passing through point $D(1,0)$ intersects the ellipse $C$ at points $P$ and $Q$ (distinct from point $A$). When the slope of the line $l$ does not exist, $|PQ| = 3$.  
$(1)$ Find the equation of the ellipse $C$;  
$(2)$ Find the range of values for the area of $\triangle APQ$.

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