
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 $C$: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)$ with an eccentricity of $\frac{\sqrt{2}}{2}$, and it passes through point $M(-2, 0)$.
(I) Find the standard equation of ellipse $C$;
(II) Let line $l$ with a slope of $1$ intersect ellipse $C$ at points $A(x\_1, y\_1)$ and $B(x\_2, y\_2)$. Connect $MA$ and $MB$, then extend them to intersect line $x = 4$ at points $P$ and $Q$. Let $y\_P$ and $y\_Q$ be the y-coordinates of points $P$ and $Q$ respectively, and $\frac{1}{y\_1} + \frac{1}{y\_2} = \frac{1}{y\_P} + \frac{1}{y\_Q}$. Find the area of triangle $ABM$.

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