
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
In the cartesian coordinate system xOy, an ellipse C is given by the equation $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1 (a>b>0). The left and right focal points of the ellipse are F<sub>1</sub> and F<sub>2</sub> respectively, with |F<sub>1</sub>F<sub>2</sub>|=2. P is any point on the ellipse C that satisfies |PF<sub>1</sub>|+|PF<sub>2</sub>|=2 $$\sqrt {2}$$.
(I) Find the standard equation of the ellipse C.
(II) Let line l: y=kx+m intersect with ellipse C at points A and B such that |AB|=2. M is the midpoint of line segment AB. Find the maximum value of |OM|.

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