
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 an ellipse $C: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \ (a > b > 0)$ whose minor axis is 2 and eccentricity is $\frac{\sqrt{2}}{2}$. Suppose a line $l$ passing through the right focus of the ellipse intersects it at two distinct points $A$ and $B$. Perpendiculars $AP$ and $BQ$ are drawn to the line $x=2$, with $P$ and $Q$ as the foot of the perpendiculars respectively. Let $\lambda = \frac{AP + BQ}{PQ}$. If the slope $k$ of line $l$ satisfies $k \geq \sqrt{3}$, then the range of values for $\lambda$ is ______.

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