
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 of radius $6$ units, $CD$ and $AB$ are perpendicular diameters. A chord $CH$ cutting $AB$ at $K$ is $10$ units long. The diameter $AB$ is divided into two segments whose dimensions are?
**A)** $5.67, 6.33$  
**B)** $4.68, 7.32$  
**C)** $4.5, 7.5$  
**D)** $6.7, 5.3$  
**E)** $6 - \sqrt{11}, 6 + \sqrt{11}$

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