
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 an ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ with left and right foci $F_{1}$, $F_{2}$, and an eccentricity of $e$. Line $l$: $y=ex+a$ intersects the $x$-axis and $y$-axis at points $A$ and $B$, respectively. $M$ is a common point between line $l$ and ellipse $C$, and $P$ is the reflection of point $F_{1}$ about line $l$. Assume $\overrightarrow{AM}=λ \overrightarrow{AB}$.
(I) If $λ= \frac{3}{4}$, find the eccentricity of ellipse $C$.
(II) If $\triangle PF_{1}F_{2}$ is isosceles, find the value of $λ$.

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