
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 $C\_1$: $\frac{x^2}{4} + \frac{y^2}{b^2} = 1 (0 < b < 2)$ with an eccentricity of $\frac{\sqrt{3}}{2}$, and the parabola $C\_2$: $x^2 = 2py (p > 0)$ with a focus that coincides with the vertex of the ellipse.
(1) Find the equation of the parabola;
(2) Find the equation of the tangent line $l$ passing through the point $M(-1, 0)$.

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