
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 the diagram below. What is $ST$?

[asy]
pair P,S,T;
P = (0,0);
S = (6,0);
T = (0,6*tan(acos(0.5)));
draw(P--S--T--P);
draw(rightanglemark(S,P,T,18));
label("$P$",P,SW);
label("$S$",S,SE);
label("$T$",T,N);
label("$10$",S/2,S);
[/asy]

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