
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
$\Delta ABC$ is isosceles with $AC = BC$. If $m\angle C = 50^{\circ}$, and point $D$ is located on $AB$ such that $AD = DB$, find the measure of $m\angle BDC$.
[asy]
pair A,B,C,D,E;
C = dir(65); B = C + dir(-115); D = midpoint(A--B); E = (2,0);
draw(B--C--A--cycle); dot(D);
label("$A$", A, S); label("$B$", B, S); label("$C$", C, N); label("$D$", D, S);
[/asy]

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