
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 Cartesian coordinate system $xOy$, it is known that the line 
$$
\begin{cases} 
x=-\frac{3}{2}+\frac{\sqrt{2}}{2}l\\
y=\frac{\sqrt{2}}{2}l
\end{cases}
$$
(with $l$ as the parameter) intersects with the curve 
$$
\begin{cases} 
x=\frac{1}{8}t^{2}\\
y=t
\end{cases}
$$
(with $t$ as the parameter) at points $A$ and $B$. Find the length of the segment $AB$.

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