
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 point \( B(0,1) \), points \( P \) and \( Q \) are any two points other than point \( B \) on the ellipse \(\frac{x^{2}}{4} + y^{2} = 1\), and \( BP \perp BQ \).
(I) If the projection of point \( B \) onto line segment \( PQ \) is point \( M \), find the equation of the locus of \( M \);
(II) Find the range of values for the intercept of the perpendicular bisector \( l \) of line segment \( PQ \) on the \( x \)-axis.

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