
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 $y^{2}=4x$ and the point $M(6,0)$, with $O$ being the coordinate origin. The line $l$ passes through point $M$ and intersects the parabola at points $A$ and $B$.

1. Find the dot product of $\overrightarrow{OA}$ and $\overrightarrow{OB}$;
2. If the area of $\triangle OAB$ is equal to $12 \sqrt{10}$, find the equation of line $l$.

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