
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 $F$ be the focus of the parabola $C: y^2 = 4x$. A line $l$ passing through point $P(-1, 0)$ intersects the parabola $C$ at points $A$ and $B$. Let $Q$ be the midpoint of segment $AB$. If $|FQ| = 2\sqrt{3}$, then the slope of line $l$ is \_\_\_\_\_\_.

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