
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
Let  $AB$  be a diameter of a circle and let  $C$  be a point on the segement  $AB$  such that  $AC : CB = 6 : 7$ . Let  $D$  be a point on the circle such that  $DC$   is perpendicular to  $AB$ . Let  $DE$  be the diameter through  $D$ . If  $[XYZ]$  denotes the area of the triangle  $XYZ$ , find  $[ABD]/[CDE]$  to the nearest integer.

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