
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 a circle with center $O$, $DE$ is a diameter, $BCD$ is a chord, $DO = 5$, and $\angle DBE = \text{arc } CE = 90^\circ$. Find the length of $BC$.
[asy]
import graph;

unitsize(2 cm);

pair O, B, C, D, E;

O = (0,0);
E = dir(30);
C = dir(220);
D = (3*C + E)/4;
B = -E;

draw(Circle(O,1));
draw(C--D--E);
draw(B--O);

label("$E$", E, NE);
label("$C$", C, W);
label("$B$", B, SW);
label("$D$", D, SE);
label("$O$", O, S);
[/asy]

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