
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 line $l$ intersects the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ at points $M$ and $N$, the midpoint $P$ of line segment $MN$ lies on the line $x = -1$. Also, the perpendicular bisector of line segment $MN$ intersects the $x$-axis at point $Q(-\frac{3}{4}, 0)$. Find the eccentricity of the ellipse $E$.

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