
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 C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ with an eccentricity of $$\frac {1}{2}$$, and it passes through point $$M(0, \sqrt {3})$$.

(I) Find the equation of ellipse C.
(II) Two perpendicular lines, l₁ and l₂, pass through point M. The distances from a point P on ellipse C to l₁ and l₂ are d₁ and d₂, respectively. Find the maximum value of $$\sqrt {d_{1}^{2}+d_{2}^{2}}$$ and the coordinates of point P in this case.

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