
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 the diagram below, point \(S\) is on the horizontal diameter of a circle centered at \(P\), and \(R\) is another point on the circumference such that $\sin \angle RPQ = \frac{3}{5}$. If \(Q\) is the right endpoint of the diameter, what is $\cos \angle RPS$?

[asy]
pair R, P, Q, S;
S = (-2,0);
P = (0,0);
Q = (2,0);
R = rotate(aSin(3/5))*(2,0);
dot("$S$", S, W);
dot("$Q$", Q, E);
dot("$R$", R, N);
dot("$P$", P, S);
draw(Q--S);
draw(P--R);
[/asy]

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