
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 $7$ units, $CD$ and $AB$ are perpendicular diameters. A chord $CH$ cutting $AB$ at $K$ is $12$ units long. Determine the lengths of the segments into which the diameter $AB$ is divided by $K$.
A) $7 - \sqrt{10}, 7 + \sqrt{10}$
B) $7 - \sqrt{13}, 7 + \sqrt{13}$
C) $6 - \sqrt{13}, 6 + \sqrt{13}$
D) $7, 7$

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