
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 hyperbola $$\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1$$ (a > 0, b > 0) with foci F₁(0, -c) and F₂(0, c), and the parabola $$y = \frac{1}{4c}x^{2}$$ whose directrix intersects the hyperbola at points M and N, find the eccentricity of the ellipse $$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{c^{2}} = 1$$.

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