
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 $A$, $B$, $C$, $D$, $E$, and $F$ lie on the circle shown. The measures of arcs $AB$, $BC$, and $CD$ are $24^\circ$, $36^\circ$, and $40^\circ$, respectively. Additionally, point $P$ lies outside the circle on the extension of line $CF$. Evaluate the sum of the angles $\angle Q$ and $\angle P$, where $\angle Q$ is the angle at point $C$ formed by the points $B$ and $D$, and $\angle P$ is the angle at point $P$ formed by lines $PC$ and $PF$.

[asy]
import graph;
unitsize(2 cm);

pair A, B, C, D, E, F, P, Q;

A = dir(160);
B = dir(120);
C = dir(80);
D = dir(0);
E = dir(-80);
F = dir(-120);
P = (2,2);
draw(Circle((0,0),1));
draw(C--P);
draw(F--P);

label("$A$", A, NW);
label("$B$", B, NE);
label("$C$", C, N);
label("$D$", D, E);
label("$E$", E, SE);
label("$F$", F, SW);
label("$P$", P, NE);
[/asy]

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