
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 $\cos S = 0.5$ in a right triangle where $SP = 10$. What is $SR$?

[asy]
pair S,P,R;
S = (0,0);
P = (10,0);
R = (0,10*tan(acos(0.5)));
draw(S--P--R--S);
draw(rightanglemark(S,P,R,18));
label("$S$",S,SW);
label("$P$",P,SE);
label("$R$",R,N);
label("$10$",P/2,S);
[/asy]

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