
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 triangle and a regular pentagon are coplanar and share a common side $\overline{AB}$, as illustrated. What is the degree measure of exterior angle $BAC$?

[asy]
for(int i=0; i < 5; ++i) {
draw(dir(360*i/5+108)--dir(360*(i+1)/5+108)); 
}
pair B = dir(360*2/5+108); // B point on pentagon
pair A = dir(360*3/5+108); // A shared vertex
pair C = dir(-144)*(A-B) + B; // Triangle's other vertex

draw(A--B--C--cycle);

label("$A$", A, NE);
label("$B$", B, W);
label("$C$", C, SW);
[/asy]

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