
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 $y^{2}=2x$, and a line $l$ that passes through the point $(0,2)$ intersecting the parabola at points $M$ and $N$. $O$ is the origin of the coordinate, and $\overrightarrow{OM} \cdot \overrightarrow{ON}=0$. Find the equation of line $l$.

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