
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 the ellipse $C: \frac{x^2}{4} + y^2 = 1$, point $P$ is any point on ellipse $C$, and point $M$ satisfies $\begin{cases} x_M = 2\lambda x_P \\ y_M = \lambda y_P \end{cases}$ $(\lambda > 1, \lambda$ is a constant$)$. When point $P$ moves on ellipse $C$, point $M$ forms curve $C_\lambda$.  
(I) Determine the equation of the trajectory for curve $C_\lambda$;  
(II) Through point $M$ on curve $C_\lambda$, draw two tangent lines MA and MB to ellipse $C$ with the tangent points A and B, respectively.  
① If the coordinates of tangent point A are $(x_1, y_1)$, find the equation of tangent line MA;  
② As point $M$ moves, is there a fixed circle that is always tangent to line $AB$? If such a circle exists, find its equation; if not, provide a reason.

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