
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
Let ellipse C be defined by $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ and it passes through the point (0, 4) with an eccentricity of $$\frac {3}{5}$$.
(Ⅰ) Find the equation of C;
(Ⅱ) Find the equation of the trajectory of the midpoint of the line segment intercepted by C and a moving line passing through the point (3, 0).

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