
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 square and an equilateral triangle share a common vertex, as shown in the diagram. The vertex shared is $C$, and the points are labeled such that $D$ is another vertex of the square, and $B$ is another vertex of the triangle. Determine the number of degrees in $m\angle CDB$.
[asy]
pair C,D,B;
C = (0,0);
D = (1,0);
B = rotate(60, C) * D;
draw(B--C--D);
label("C", C, SW);
label("D", D, SE);
label("B", B, N);
[/asy]

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