
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 C: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\ (a > b > 0)$$ passing through the point (0, 4) with an eccentricity of $$\frac{3}{5}$$

1. Find the equation of C;
2. Find the coordinates of the midpoint of the line segment intercepted by C on the line passing through the point (3, 0) with a slope of $$\frac{4}{5}$$.

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