
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, $EF$ and $GH$ are perpendicular diameters. A chord $EJ$ that cuts $GH$ at $M$ is $10$ units long. What are the lengths of the two segments into which the diameter $GH$ is divided?
- **A)** $4, 8$
- **B)** $5, 7$
- **C)** $6 - \sqrt{11}, 6 + \sqrt{11}$
- **D)** $3, 9$
- **E)** $10 - \sqrt{30}, 10 + \sqrt{30}$

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