
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 parabola with its vertex at the origin $O$ and focus on the $x$-axis, its inscribed triangle $\triangle ABC$ has its centroid as the focus $F$. The equation of the line $BC$ is $4x + y - 20 = 0$.
(1) Find the equation of the parabola;
(2) A tangent line $l$ is drawn to the parabola at a moving point $M$, intersecting the parabola at another point $N$ with $MN \perp l$. A line segment $ME$ is drawn parallel to the $x$-axis with $E$ on the right side of $M$. If $\angle FMN = \lambda \angle NME$, find the value of $\lambda$.

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