
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
In the diagram, $\angle XYZ = \angle XZY$. If $ZY = 8$ and $XZ = 10$, what is the perimeter of $\triangle XYZ$? [asy]
draw((0,0)--(5,8.66)--(10,0)--cycle);
label("8",(5,0),S);
label("$Z$",(0,0),SW);
label("$Y$",(10,0),SE);
label("$X$",(5,8.66),N);
label("10",(7.5,4.33));
[/asy]

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