
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 an ellipse: $$\frac {y^{2}}{a^{2}} + \frac {x^{2}}{b^{2}} = 1$$ ($a > b > 0$), with eccentricity $$\frac {\sqrt {2}}{2}$$, and foci $F_1(0, -c)$, $F_2(0, c)$. A line passing through $F_1$ intersects the ellipse at points M and N, and the perimeter of $\triangle F_2MN$ is 4.

(I) Find the equation of the ellipse;  
(II) A line $l$, which does not coincide with the y-axis, intersects the y-axis at point $P(0, m)$ ($m \neq 0$), and intersects the ellipse $C$ at two distinct points $A$ and $B$, with $\overrightarrow {AP} = \lambda \overrightarrow {PB}$. If $\overrightarrow {OA} + \lambda \overrightarrow {OB} = 4 \overrightarrow {OP}$, find the range of values for $m$.

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