
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
The parabola $C: y^2 = 2px$ ($p > 0$) has a focus $F$. Point $A$ is on $C$, and the distance from $A$ to $F$ is twice the distance from $A$ to the $y$-axis. If the area of triangle $OAF$ (where $O$ is the origin) is $1$, calculate the value of $p$.

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