
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 with a radius of $7$ units, $CD$ and $AB$ are perpendicular diameters. A chord $CH$ intersecting $AB$ at $K$ is $12$ units long. Determine the dimensions of the two segments into which the diameter $AB$ is divided.
A) $\sqrt{7}, 14 - \sqrt{7}$
B) $\sqrt{10}, 14 - \sqrt{10}$
C) $\sqrt{13}, 14 - \sqrt{13}$
D) $\sqrt{15}, 14 - \sqrt{15}$

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