
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
A circle $C$: $(x-2)^2+y^2=4$, a line $l\_1$: $y= \sqrt {3}x$, $l\_2$: $y=kx-1$. If the length ratio of the chords intercepted by $l\_1$ and $l\_2$ on the circle $C$ is $1:2$, then the value of $k$ is $\_\_\_\_\_\_\_\_$.

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