
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
Let vector $\overrightarrow{a} = (0, 2)$, $\overrightarrow{b} = (1, 0)$. A line passing through the fixed point A(0, -2) with direction vector $\overrightarrow{a} + \lambda \overrightarrow{b}$ intersects with another line passing through point B(0, 2) with direction vector $\overrightarrow{b} - 2\lambda \overrightarrow{a}$ at point P, where $\lambda \in \mathbb{R}$,

(Ⅰ) Find the equation of the trajectory C of point P;

(Ⅱ) Suppose a line $l$ passing through E(1, 0) intersects with C at two distinct points M and N, find the range of values for $\overrightarrow{EM} \cdot \overrightarrow{EN}$.

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