
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 $y=x^{2}$ with focus $F$, a line $l$ passes through a point $N$ on the positive half of the $y$-axis and intersects the parabola at points $A$ and $B$. It is also given that $\overrightarrow{OA} \cdot \overrightarrow{OB}=2$ (where $O$ is the origin). The symmetric point of $F$ with respect to the line $OA$ is $C$. Find the minimum value of the area of quadrilateral $OCAB$.

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