
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 that F is the focus of the parabola x²=8y, and points A, B, and C lie on this parabola. If $\overrightarrow {FA}+ \overrightarrow {FB}+ \overrightarrow {FC}=0$, then find the value of $| \overrightarrow {FA}|+| \overrightarrow {FB}|+| \overrightarrow {FC}|$.

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