
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 point P ($$\sqrt {3}$$, $$\frac {1}{2}$$) with an eccentricity of $$\frac { \sqrt {3}}{2}$$.
(1) Find the standard equation of the ellipse C.
(2) If a line l intersects the ellipse C at points A and B, and the midpoint of segment AB is ($$\frac {1}{2}$$, $$\frac {1}{2}$$), find the area of the triangle formed by line l and the coordinate axes.

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