
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
Given that point P lies on the line $x-2y-1=0$ and point Q lies on the line $x-2y+3=0$, if the midpoint of line segment PQ is $M(x_0, y_0)$ and $y_0 > -x_0 + 2$, find the range of values for $\sqrt{(x_0-4)^2 + y_0^2}$.

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