
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
An equilateral triangle $ABC$ and a regular pentagon $BCDEF$ are coplanar, as shown. Determine the measure of angle $CAD$.

[asy]
size(100);
pair B = dir(180);
pair C = dir(108);
pair D = dir(36);
pair E = dir(-36);
pair F = dir(-108);
pair A = extension(B, rotate(60, B)*C, C, rotate(60, C)*B);
draw(A--B--C--D--E--F--cycle);
draw(A--C);
draw(A--D);
label("$A$", A, N);
label("$B$", B, NW);
label("$C$", C, NE);
label("$D$", D, E);
label("$E$", E, SE);
label("$F$", F, SW);
[/asy]

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