
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 $\Delta ABC$, $CD \parallel AB$ and $m\angle DCB = 50^\circ$. Determine the number of degrees in $m\angle BCD$.
[asy]
pair A,B,C,D,E;
B = dir(-40);
A = dir(-140);
D = (.5,0);
E = .4 * dir(40);
draw(C--B--A--E,EndArrow);
draw(C--D,EndArrow);
label("$A$",A,W);
label("$C$",C,NW);
label("$B$",B,E);
label("$D$",D,E);
label("$E$",E,E);
[/asy]

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