
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 with radius 3 is tangent to a circle with radius 4. The sides of $\triangle XYZ$ are tangent to the circles so that $|XZ|=|XY|$. Determine the area of $\triangle XYZ$.

[asy]
unitsize(0.8 cm);
pair X,Y,Z;
X=(0,12);
Y=(-3.6,0);
Z=(3.6,0);
draw(X--Y--Z--cycle,linewidth(0.7));
draw(Circle((0,3),3),linewidth(0.7));
draw(Circle((0,7.5),1.5),linewidth(0.7));
draw((0,3)--(3,3),linewidth(0.5)); // Makes smaller circle, radius line
draw((0,7.5)--(1.5,7.5),linewidth(0.5)); // Makes larger circle, radius line
label("4",(1.5,3),N);
label("3",(0.75,7.5),N);
label("$X$",X,N);
label("$Y$",Y,SW);
label("$Z$",Z,SE);
[/asy]

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