
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
In the rectangular coordinate system, the parametric equations of line $l$ are given by $ \begin{cases} x=-2-3t \\ y=2-4t \end{cases} (t\text{ is the parameter}) $. The line intersects curve $C$: $(y-2)^{2}-x^{2}=1$ at points $A$ and $B$. Find the distance between points $A$ and $B$, denoted as $|AB|$.

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