
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
In the Cartesian coordinate system $xOy$, a perpendicular line $l$ is drawn from the right focus $F$ of the hyperbola $C: x^{2}-\frac{y^{2}}{3}=1$ to the $x$-axis. The area of the triangle formed by the line $l$ and the two asymptotes of the hyperbola $C$ is \_\_\_\_.

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