
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 $y^{2}=4x$, a line $l$ passing through its focus $F$ intersects the parabola at points $A$ and $B$ (with point $A$ in the first quadrant), such that $\overrightarrow{AF}=3\overrightarrow{FB}$. A line passing through the midpoint of $AB$ and perpendicular to $l$ intersects the $x$-axis at point $G$. Calculate the area of $\triangle ABG$.

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