
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
Point M is on the ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$ ($a>b>0$), and a circle centered at M is tangent to the x-axis at the right focus F of the ellipse.  
(I) If the circle M intersects the y-axis at points A and B, and $\triangle ABM$ is an equilateral triangle with side length 2, find the equation of the ellipse;  
(II) Given point F(1,0), let line l pass through point F and intersect the ellipse at points C and D. If, when line l rotates around point F, it always holds that $|OC|^{2}+|OD|^{2}<|CD|^{2}$, find the range of the real number a.

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