
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. Another chord, $CH$, intersects the diameter $AB$ at the point $K$, $3$ units away from $A$. The chord $CH$ has a length of $12$ units. Find the lengths of the two segments $AK$ and $KB$.
A) $4, 10$
B) $3, 11$
C) $5, 9$
D) $3.5, 10.5$
E) None of the above

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