
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 that $F_1$ and $F_2$ are the left and right foci of the ellipse E: $$\frac {x^{2}}{a^{2}}$$ + $$\frac {y^{2}}{b^{2}}$$ = 1 ($a > b > 0$), and point P($-1$, $$\frac { \sqrt {2}}{2}$$) is on ellipse E. The focus of the parabola $y^2 = 4x$ is one focus of the ellipse E.

(I) Find the standard equation of ellipse E.
(II) A line $l$ passing through point $F_2$ is drawn, not parallel to the x-axis, intersecting with the circle $x^{2}+y^{2} = a^{2} + b^{2}$ at points A and B, and with ellipse E at points C and D. When $$\overrightarrow {F_{1}A}$$ $\cdot$ $$\overrightarrow {F_{1}B}$$ = 1, find the area of triangle $F_1CD$.

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