
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 the right triangles PQR and PRS, what is the length of segment QR, in units?
```
size(150);
pair P, Q, R, S, X;
P=(0,0);
Q=(0,15);
R=(-20,0);
S=(-45,0);
draw(P--Q--S--P);
draw(Q--R);
draw((0,2)--(-2,2)--(-2,0));
label("$51$", (Q+S)/2, NW);
label("$25$", (R+S)/2, S);
label("$20$", (P+R)/2, S);
label("P", P, SE);
label("Q", Q, NE);
label("S", S, SW);
label("R", R, S);
```

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