
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
A circle of radius 2 is tangent to a circle of radius 3. The sides of $\triangle PQR$ are tangent to these circles, and the sides $\overline{PQ}$ and $\overline{PR}$ are congruent. What is the area of $\triangle PQR$?

[asy]
unitsize(0.7cm);
pair P,Q,R;
P=(0,10);
Q=(-3.6,0);
R=(3.6,0);
draw(P--Q--R--cycle,linewidth(0.7));
draw(Circle((0,3),3),linewidth(0.7));
draw(Circle((0,7),2),linewidth(0.7));
draw((0,3)--(3,3));
draw((0,7)--(2,7));
label("3",(2,3),N);
label("2",(1,7),N);
label("$P$",P,N);
label("$Q$",Q,SW);
label("$R$",R,SE);
[/asy]

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