
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 a point $P(x_{0},y_{0}) (x_{0} \neq \pm a)$ on the ellipse $E: \dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$, where $M$ and $N$ are the left and right vertices of the ellipse $E$. The product of the slopes of the lines $PM$ and $PN$ is $-\dfrac{1}{4}$.

1. Find the eccentricity of ellipse $E$.
2. A line passing through the left focus of ellipse $E$ with a slope of $1$ intersects ellipse $E$ at points $A$ and $B$. $O$ is the origin, and point $C$ is a point on ellipse $E$ that satisfies $\overrightarrow{OC} = λ \overrightarrow{OA} + \overrightarrow{OB} (λ \neq 0)$. Find the value of $λ$.

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