
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 points A($x_1$, $y_1$), B($x_2$, $y_2$), and C($x_3$, $y_3$) on the parabola $x^2 = 4y$, the focus F of the parabola satisfies $\overrightarrow{FA} + \overrightarrow{FB} + \overrightarrow{FC} = \overrightarrow{0}$. Determine the value of $k_{AB} + k_{AC} + k_{BC} =\_\_\_\_\_\_.$

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