
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 a straight line $l$ intersects the parabola $C: y^2 = 2px$ ($p > 0$) at points $A$ and $B$, and $\angle AOB = 90^\circ$, where point $O$ is the origin and point $A$ has coordinates $(1, 2)$.
(I) Find the equation of the parabola $C$;
(II) Find the coordinates of point $B$.

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