
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 hyperbola $C: \dfrac{x^2}{4} - y^2 = 1$, the left and right vertices are $A_1$ and $A_2$ respectively. Points $P$ and $Q$ move on curve $C$ and are symmetrical with respect to the x-axis. The line $A_1P$ intersects with line $A_2Q$ at point $M$.
(1) Find the equation of the trajectory $D$ of the moving point $M$.
(2) Given the point $E(0,2)$, for points $A, B$ on the trajectory $D$, satisfying $\vec{EA} = \lambda \vec{EB}$, find the range of the real number $\lambda$.

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