
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
Suppose that there are three congruent triangles $\triangle ABC$, $\triangle ACD$, and $\triangle ADE$ such that $AB = AC = AD = AE,$ as shown in the following diagram. If $\angle BAC = 30^\circ,$ then what is $\angle BDE$? [asy]
pair pA, pB, pC, pD, pE;
pA = (0, 0);
pB = pA + dir(230);
pC = pA + dir(250);
pD = pA + dir(270);
pE = pA + dir(290);
draw(pA--pB--pC--pA);
draw(pA--pC--pD--pA);
draw(pA--pD--pE--pA);
label("$A$", pA, N);
label("$B$", pB, SW);
label("$C$", pC, S);
label("$D$", pD, TW);
label("$E$", pE, TR);
[/asy]

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