
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
Let A, B, C be three points on the parabola x²=4y, point F be the focus of the parabola, and point N be the midpoint of AB.
(I) If $\overrightarrow {CF}$=2 $\overrightarrow {FN}$, find the value of $| \overrightarrow {FA}|+| \overrightarrow {FB}|+| \overrightarrow {FC}|$;
(II) If $\overrightarrow {CF}$=3 $\overrightarrow {FN}$, find the maximum area of △ABC.

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