
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
A regular equilateral triangle shares a common side with a rectangle. The adjacent side of the rectangle, which is perpendicular to the shared side, is twice the length of the shared side. What is the number of degrees in $m\angle CDB$? 
[asy] 
pair A,E,C,D,B; 
D = dir(60); 
C = dir(0); 
E = (0,-2); 
B = C+E; 
draw(B--D--C--B--E--A--C--D--A); 
label("D",D,N); 
label("C",C,dir(0)); 
label("B",B,dir(0));
[/asy]

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