
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
Suppose $\cos R = \frac{5}{13}$ in the diagram below. What is $QS$?

[asy]
pair Q,R,S;
S = (0,0);
Q = (sqrt(194),0);
R = (sqrt(194),-5);
draw(S--Q--R--S);
draw(rightanglemark(S,Q,R,13));
label("$S$",S,NW);
label("$Q$",Q,NE);
label("$R$",R,SE);
label("$13$",(R+S)/2,SW);
[/asy]

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