
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 plane $(xOy)$, the line $l$ is defined by the parametric equations $\begin{cases}x=1+\frac{3}{5}t, \\ y=\frac{4}{5}t\end{cases}(t\in\mathbb{R})$, and the curve $C$ is defined by the parametric equations $\begin{cases}x=4k^2, \\ y=4k\end{cases}(k\in\mathbb{R})$. The line $l$ intersects the curve $C$ 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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