
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 E: x² + 2y² = 8, the line l intersects E at points P and Q, l intersects the x-axis and y-axis at points C and D respectively, and O is the origin of the coordinate system.
(I) Find the length of the major axis and the eccentricity of the ellipse.
(II) Determine if there exists a line l that satisfies the conditions: $$\begin{cases} \overrightarrow {OD}= \frac {1}{3} \overrightarrow {OP}+ \frac {2}{3} \overrightarrow {OQ} \\ \overrightarrow {OC}= \frac {1}{3} \overrightarrow {OQ}+ \frac {2}{3} \overrightarrow {OP}\end{cases}$$, if so, find the equation of line l; if not, explain the reason.

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