
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
Triangle $PQR$ is similar to triangle $XYZ$ and triangle $XYZ$ is similar to triangle $GHI$. If $PQ = 5$, $QR = 15$, and $HI = 30$ units, what is the length of segment $XY$?

[asy]
draw((0,0)--(5,0));
draw((0,0)--(0,3));
draw((0,3)--(5,0));
label("P",(0,0),W);
label("Q",(5,0),E);
label("R",(0,3),W);

draw((10,0)--(17.5,0));
draw((10,0)--(10,4.5));
draw((10,4.5)--(17.5,0));
label("X",(10,0),W);
label("Y",(17.5,0),E);
label("Z",(10,4.5),W);

draw((23,0)--(34.5,0));
draw((23,0)--(23,6));
draw((23,6)--(34.5,0));
label("G",(23,0),W);
label("H",(34.5,0),E);
label("I",(23,6),W);
[/asy]

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