
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
Equilateral $\triangle ABC$ is inscribed in a circle of radius $3$. Extend $\overline{AB}$ through $B$ to point $D$ such that $AD = 15,$ and extend $\overline{AC}$ through $C$ to point $E$ such that $AE = 13.$ Through $D,$ draw a line $l_1$ parallel to $\overline{AE},$ and through $E,$ draw a line $l_2$ parallel to $\overline{AD}.$ Let $F$ be the intersection of $l_1$ and $l_2.$ Let $G$ be the point on the circle that is collinear with $A$ and $F$ and distinct from $A.$ Calculate the area of $\triangle CBG$ and express it in the form $\frac{p\sqrt{q}}{r},$ identifying $p$, $q$, and $r$ as described.

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