
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 its two foci being F<sub>1</sub> and F<sub>2</sub>, and |F<sub>1</sub>F<sub>2</sub>|=2. Point P is on the ellipse, and the perimeter of △PF<sub>1</sub>F<sub>2</sub> is 6.
(Ⅰ) Find the equation of ellipse C;
(Ⅱ) If the coordinates of point P are (2,1), and a line l (not passing through the origin O) intersects ellipse C at points A and B, with the midpoint of segment AB being M, and the distance from point P to line l being d, and points M, O, P are collinear. Find the maximum value of $$\frac {12}{13}|AB|^{2}+ \frac {13}{16}d^{2}$$.

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