
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 $C$: $y^{2}=2px (p > 0)$ passes through the point $P(1,-2)$.
(I) Find the equation of the parabola $C$ and its axis equation;
(II) The line $l$ passing through the focus $F$ with a slope of $2$ intersects the parabola at points $A$ and $B$. Find the area of $\triangle OAB$.

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