
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
Let $AB$ be a diameter of a circle centered at $O$. Let $F$ be a point on the circle, and let the tangent at $B$ intersect the tangent at $F$ and $AF$ at $C$ and $D$, respectively. Let $G$ be another point on the same circle where another tangent to the circle at $G$ intersects the extended line $AF$ at point $H$. If $\angle BAF = 30^\circ$, find $\angle CHD$, in degrees.

[asy]
import graph;

unitsize(2 cm);

pair O, A, B, C, D, F, G, H;

O = (0,0);
A = (0,1);
B = (0,-1);
F = dir(-30);
G = dir(120);
D = extension(A,F,B,B + rotate(90)*(B));
C = extension(F,F + rotate(90)*(F),B,B + rotate(90)*(B));
H = extension(A,F,G,G + rotate(90)*(G));

draw(Circle(O,1));
draw(B--A--D--C--H--G--cycle);
draw(B--F--C);

label("$A$", A, N);
label("$B$", B, S);
label("$C$", C, S);
label("$D$", D, SE);
label("$F$", F, dir(-30));
label("$G$", G, dir(120));
label("$H$", H, N);
dot("$O$", O, W);
[/asy]

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