
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 another point on the circle, and let the tangent at $B$ intersect the tangent at $F$ and $AF$ at $G$ and $H$, respectively. If $\angle BAF = 37^\circ$, find $\angle HGF$, in degrees.

```asy
import graph;
unitsize(2 cm);

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

O = (0,0);
A = (0,1);
B = (0,-1);
F = dir(145);
H = extension(A,F,B,B + rotate(90)*(B));
G = extension(F,F + rotate(90)*(F),B,B + rotate(90)*(B));

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

label("$A$", A, N);
label("$B$", B, S);
label("$G$", G, S);
label("$H$", H, NW);
label("$F$", F, dir(145));
dot("$O$", O, dir(270));
```

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