
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 the parametric equation of line $l$ as $$\begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$$ ($t$ is the parameter), and $l$ intersects with the circle $x^2+y^2-4x+3=0$ at points $A$ and $B$, with $|AB|=\sqrt{3}$. Determine the slope of line $l$.

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