
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 parabola $y^{2}=2px(p > 0)$, a line $l$ passing through point $C(-2,0)$ intersects the parabola at points $A$ and $B$, with the origin denoted as $O$, and $\overrightarrow{OA} \cdot \overrightarrow{OB}=12$  
(Ⅰ) Find the equation of the parabola;  
(Ⅱ) When the area of the circle with diameter $AB$ is $16\pi$, find the area $S$ of $\triangle AOB$.

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