
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
In $\triangle ABC$, $AC = BC$, $AB = BC$, $m\angle ACB = 60^{\circ}$, and $CD$ is the altitude from point $C$ to line $AB$. Point $E$ is the midpoint of $CD$. What is the number of degrees in $m\angle ECB$?

[asy]
pair A,B,C,D,E; 
A = (-1,0);
B = (1,0);
C = (0, 1.732/2);
D = (0, 0);
E = (0, 1.732/4);
draw(A--B--C--cycle);
draw(C--D);
dot("$A$", A, SW);
dot("$B$", B, SE);
dot("$C$", C, N);
dot("$D$", D, S);
dot("$E$", E, E);
[/asy]

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