
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 a parabola with its vertex at the origin and its focus $F$ on the $y$-axis. Also, a point $P(k, -2)$ on the parabola is at a distance of $4$ from the focus. Find the value of $k$. (　　)

**A．** $4$           **B．** $4$ or $-4$          **C．** $-2$             **D．** $-2$ or $2$

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