
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 a point $D$ lies on line $BC$ such that $AD$ is an altitude of $\Delta ABC$, what is the number of degrees in $m\angle ADB$?

    [asy]
    pair A,B,C,D;
    B = dir(110);
    C = dir(70);
    A = (0,0);
    D = midpoint(B--C);
    draw(A--B--C--cycle);
    draw(A--D);
    label("$A$", A, S);
    label("$B$", B, W);
    label("$C$", C, E);
    label("$D$", D, N);
    markscalefactor=0.05;
    draw(rightanglemark(A,D,C));
    [asy]

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