
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
A circle has $(2, 4)$ and $(10, 8)$ as endpoints of its diameter and intersects a line $y = -\frac{1}{2}x + 5$. Determine the x-coordinates of the points of intersection of the circle with this line.
A) $4.4 + 2.088$
B) $4.4 - 2.088$
C) $6.488$
D) $2.312$

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