
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 one focus of the ellipse C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}$$\=1 (a>b>0) coincides with the focus of the parabola y<sup>2</sup>\=4 $$\sqrt {3}x$$, and the eccentricity is $$\frac { \sqrt {3}}{2}$$.

1. Find the standard equation of the ellipse C.
2. The line l, which does not pass through the origin, intersects the ellipse C at points M and N. If the slopes of the three lines OM, l, and ON form a geometric sequence with common ratio k<sub>1</sub>, k, and k<sub>2</sub>, find the slope of line l and the value of |OM|<sup>2</sup>+|ON|<sup>2</sup>.

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