
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 $ABC$ shares a common side $BC$ with a regular pentagon $BCDEF$, as pictured. Determine the number of degrees in $\angle DAE$? [asy]
pair pA, pB, pC, pD, pE, pF;
pA = (0, 0);
pB = pA + dir(300);
pC = pA + dir(240);
pD = pC + dir(282);
pE = pC + dir(354);
pF = pB + dir(18);
draw(pA--pB--pC--pA);
draw(pB--pC--pD--pE--pF--pB);
label("$A$", pA, N);
label("$B$", pB, E);
label("$C$", pC, W);
label("$D$", pD, SW);
label("$E$", pE, S);
label("$F$", pF, SE);
[/asy]

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