
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 the ellipse $\frac{y^2}{a^2} + x^2 = 1$ ($a > 1$) with an eccentricity $e = \frac{2\sqrt{5}}{5}$, let $P$ be a moving point on the ellipse. Find the maximum distance between the line connecting point $P$ and the fixed point $B(-1, 0)$.

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