
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
A regular triangle and a regular nonagon are coplanar and share a common side $\overline{AD}$. What is the degree measure of the exterior angle $BAC$?

[asy]
for(int i=0; i <=9; ++i) {
draw(dir(360*i/9+90)--dir(360*(i+1)/9+90));
}
pair A = dir(360*5/9+90);
pair D = dir(360*6/9+90);
pair C = A+dir(-30)*(D-A);
pair B = dir(360*4/9+90);

draw(A--C--D);

label("$A$",A,NE);
label("$B$",B,W);
label("$C$",C,S);
label("$D$",D,NE);

[/asy]

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