
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, $PC$ is tangent to semicircle $SAR$, $PD$ is tangent to semicircle $RBT$, and $SRT$ is a straight line. If arc $AS$ is $70^\circ$ and arc $BT$ is $45^\circ$, then find $\angle CPD$, in degrees.

[asy]
import graph;

unitsize(1.5 cm);

pair A, B, P, R, S, T, C, D;
pair[] O;
real[] r;

r[1] = 1;
r[2] = 0.8;

S = (-2*r[1],0);
O[1] = (-r[1],0);
R = (0,0);
O[2] = (r[2],0);
T = (2*r[2],0);
A = O[1] + dir(180 - 70)*r[1];
B = O[2] + dir(45)*r[2];
C = A;
D = B;
P = extension(C, C + rotate(90)*(C - O[1]), D, D + rotate(90)*(D - O[2]));

draw(S--T);
draw(arc(O[1],r[1],0,180));
draw(arc(O[2],r[2],0,180));
draw(C--P--D);

label("$C$", C, NW);
label("$D$", D, NE);
label("$P$", P, N);
label("$R$", R, dir(270));
label("$S$", S, SW);
label("$T$", T, SE);
[/asy]

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