
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 with equation $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ ($a > b > 0$), its left focus is $F$, and its upper vertex is $B$. The minor axis has a length of 4, and the eccentricity is $\frac{\sqrt{5}}{5}$.
(I) Find the equation of the ellipse.
(II) Suppose point $P$ is on the ellipse and different from the upper and lower vertices. Point $M$ is the intersection of line $PB$ and the $x$-axis, and point $N$ is on the negative half of the $y$-axis. If $|ON| = |OF|$ (where $O$ is the origin), and $OP \perp MN$, find the slope of line $PB$.

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