
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 any point on the curve $C$, its distance to the point $F(1,0)$ is equal to its distance to the line $x=-1$. The line $l$ passes through the point $A(1,1)$ and intersects $C$ at points $P$ and $Q$.
(I) Find the equation of the curve $C$.
(II) If $A$ is the midpoint of $PQ$, find the area of the triangle $OPQ$.

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