
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
Altitudes $\overline{AF}$ and $\overline{BG}$ of $\triangle ABC$ intersect at $H$. If $\angle BAC = 60^\circ$ and $\angle ABC = 80^\circ$, then what is $\angle AHB$?

[asy]
size(150); defaultpen(linewidth(0.8));
pair B = (0,0), C = (3,0), A = (1,2.5), F = foot(A,B,C), G = foot(B,A,C), H = intersectionpoint(B--G,A--F);
draw(A--B--C--cycle);
draw(A--F^^B--G);
label("$A$",A,N); label("$B$",B,W); label("$C$",C,E); label("$F$",F,S); label("$G$",G,NW); label("$H$",H,NE);
draw(rightanglemark(C,F,A,3.5));
draw(rightanglemark(H,G,A,3.5));
[/asy]

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