
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 $8$ units, $PQ$ and $RS$ are perpendicular diameters. A chord $PT$ cutting $RS$ at $M$ is $12$ units long. What are the dimensions of the two segments into which the diameter $RS$ is divided?
**A)** $4, 12$
**B)** $8 + 2\sqrt{7}, 8 - 2\sqrt{7}$
**C)** $6, 10$
**D)** $7, 9$
**E)** None of these

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