
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 $y^2=2px$ ($p>0$) with focus $F$, and the equation of the directrix is $x=-\frac{1}{2}$.  
(1) Find the equation of the parabola;  
(2) Let point $P$ be on the parabola, and $|PF|=2$. If $O$ is the origin, find the area of $\triangle OFP$.

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