
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 $$\begin{cases} x=-1+3t \\ y=2-4t \end{cases}$$ (where $t$ is the parameter), it intersects with curve $C$: $(y-2)^2-x^2=1$ at points $A$ and $B$.  
(1) Find the length of $|AB|$;  
(2) Find the distance from point $P(-1,2)$ to the midpoint $C$ of segment $AB$.

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