
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 triangle $PQR$, $PQ = 7$, $QR = 24$, and $PR = 25$.

[asy]
defaultpen(1);

pair P = (0,0), Q = (24,0), R = (24,7);
draw(P--Q--R--cycle);

label("\(P\)", P, SW);
label("\(Q\)", Q, SE);
label("\(R\)", R, N);
[/asy]

Point $S$ is randomly selected inside triangle $PQR$. What is the probability that $S$ is closer to the midpoint of $QR$ than it is to either $P$ or $R$?

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