
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 line $l$: $x-\sqrt{3}y+6=0$ and a circle $x^{2}+y^{2}=12$ intersect at points $A$ and $B$. Perpendiculars are drawn from $A$ and $B$ to the $x$-axis, meeting it at points $C$ and $D$ respectively. Find the length of $|CD|$.

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