
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) passing through the point (1, $$\frac { \sqrt {3}}{2}$$), with a focal length of 2 $$\sqrt {3}$$.
(1) Find the equation of ellipse C;
(2) The left and right foci of ellipse C are F<sub>1</sub> and F<sub>2</sub> respectively. A line l passes through point F<sub>2</sub> and intersects ellipse C at points A and B. Find the maximum area S of △F<sub>​1</sub>AB and the corresponding equation of line l.

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