
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 with the equation $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ where $a>b>0$, its eccentricity is $$\frac {\sqrt {6}}{3}$$. The distance from one end of its minor axis to the right focus is $$\sqrt {3}$$.
(1) Find the equation of ellipse C.
(2) The line $y=x+1$ intersects the ellipse at points A and B. If P is a point on the ellipse, find the maximum area of triangle PAB.

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