
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 the ellipse C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$, with two foci F<sub>1</sub> (-2, 0), F<sub>2</sub> (2, 0), and P is a moving point on the ellipse, such that the maximum value of the vector $$\overrightarrow {PF_{1}}\cdot \overrightarrow {PF_{2}}$$ is 2.  
(1) Find the equation of the ellipse;  
(2) A line l passing through the left focus intersects the ellipse C at points M and N, and satisfies $$\overrightarrow {OM}\cdot \overrightarrow {ON}sinθ= \frac {4 \sqrt {6}}{3}cosθ$$$$(θ≠ \frac {π}{2})$$, find the equation of line l (where ∠MON=θ, O is the origin).

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