
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 line $y=kx+1$ and the circle defined by the parametric equations $\begin{cases} x=2\cos\alpha \\ y=3+2\sin\alpha \end{cases}$ (where $\alpha$ is a parameter), the line intersects the circle at points M and N. If the distance between M and N is $|MN|=2\sqrt{3}$, then find the value of $k$.

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