
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
Given right triangles $PQR$ and $PRS$, what is the length of segment $QR$, in units? 
[asy]
size(150);
pair P, Q, R, S, X;
P=(0,0);
Q=(0,15);
R=(21,0);
S=(0,32);
draw(P--Q--S--P);
draw(Q--R);
draw((0,2)--(2,2)--(2,0));
label("$33$", (Q+S)/2, NW);
label("$21$", (P+R)/2, S);
label("$15$", (P+Q)/2, E);
label("P", P, SE);
label("Q", Q, NE);
label("R", R, SW);
label("S", S, N);
[/asy]

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