
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 that $F\_1$ and $F\_2$ are the left and right foci of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, and point $P(-1, \frac{\sqrt{2}}{2})$ is on the ellipse. The line segment $PF\_2$ intersects with the $y$-axis at point $M$, which satisfies $\overrightarrow{PM} = \overrightarrow{MF\_2}$.
(I) Find the standard equation of the ellipse;
(II) Draw a line $l$ passing through $F\_2$ that does not coincide with the $x$-axis. Line $l$ intersects with the circle $x^2 + y^2 = a^2 + b^2$ at points $A$ and $B$ and intersects with the ellipse at points $C$ and $D$. When $\overrightarrow{F\_1A} \cdot \overrightarrow{F\_1B} = λ$, and $λ ∈ [\frac{2}{3}, 1]$, find the range of values for the area $S$ of $\triangle F\_1CD$.

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