
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
Isosceles $\triangle ABC$ with $AB = AC$ is inscribed in a circle of radius $3$. Extend $\overline{AB}$ through $B$ to point $D$ such that $AD = 17$, and extend $\overline{AC}$ through $C$ to point $E$ such that $AE = 15$. 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 $A$. Find the area of $\triangle CBG$ and express it in the form $\frac{p\sqrt{q}}{r}$, where $p, q$, and $r$ are positive integers with $p$ and $r$ relatively prime and $q$ not divisible by the square of any prime. Report the sum $p+q+r$. Assume $BC = 6$.

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