
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
Points $A$, $B$, $R$, $D$, and $C$ lie on a circle, with $B$ and $D$ diametrically opposite each other. The measures of arcs $BR$ and $RD$ are $72^\circ$ and $108^\circ$, respectively. Find the sum of the measures of angles $P$ and $R$ in degrees.
[asy]
import graph;

unitsize(2 cm);

pair A, B, C, D, P, R;

A = dir(160);
B = dir(90);
C = dir(190);
D = dir(-90);
P = extension(A,B,C,D);
R = dir(0);

draw(Circle((0,0),1));
draw(B--P--D);
draw(A--R--C);

label("$A$", A, NW);
label("$B$", B, N);
label("$C$", C, SW);
label("$D$", D, S);
label("$P$", P, E*1.5);
label("$R$", R, E);
[/asy]

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