
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, we have $\cos \angle RPQ = \frac{24}{25}$. What is $\cos \angle RPT$ where $T$ is directly opposite to $Q$ with respect to point $P$ on a straight line?

[asy]
pair R,P,Q,T;
T = (-2,0);
P = (0,0);
Q = (2,0);
R = rotate(aCos(24/25))*(1.5,0);
dot("$T$",T,W);
dot("$Q$",Q,E);
dot("$R$",R,N);
dot("$P$",P,S);
draw(T--Q);
draw(P--R);
[/asy]

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