
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 area of triangle $\triangle OFA$, where line $l$ has an inclination angle of $60^\circ$ and passes through the focus $F$ of the parabola $y^2=4x$, and intersects with the part of the parabola that lies on the x-axis at point $A$, is equal to $\frac{1}{2}\cdot OA \cdot\frac{1}{2} \cdot OF \cdot \sin \theta$. Determine the value of this expression.

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