
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
 $DEB$  is a chord of a circle such that  $DE=3$  and  $EB=5$ . Let  $O$  be the centre of the circle. Join  $OE$  and extend  $OE$  to cut the circle at  $C$ . (See diagram). Given  $EC=1$ , find the radius of the circle.

[asy]
size(6cm);

pair O = (0,0), B = dir(110), D = dir(30), E = 0.4 * B + 0.6 * D, C = intersectionpoint(O--2*E, unitcircle);

draw(unitcircle);
draw(O--C);
draw(B--D);

dot(O);
dot(B);
dot(C);
dot(D);
dot(E);

label(" $B$ ", B, B);
label(" $C$ ", C, C);
label(" $D$ ", D, D);
label(" $E$ ", E, dir(280));
label(" $O$ ", O, dir(270));
[/asy]

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