
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 $\Delta PQR$, $\overline{ST} \parallel \overline{PQ}, PS = 7$ cm, $SR = 5$ cm, and $TQ = 3$ cm. What is the number of centimeters in the length of $\overline{PR}$?

[asy]pair P,Q,R,S,T;
P = (-3,-5); Q = (5,-5); R = (0,0); S = P/3; T = Q/3;
draw(T--S--R--Q--P--S);
label("P",P,W); label("Q",Q,dir(0)); label("R",R,N); label("S",S,W);
label("T",T,dir(0));
[/asy]

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