
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 $xoy$, the parametric equation of line $l$ is given by $\begin{cases} & x=\frac{2\sqrt{5}}{5}t \\ & y=1+\frac{\sqrt{5}}{5}t \end{cases}(l$ is the parameter$)$, and line $l$ intersects with the parabola $y^{2}=4x$ at points $A$ and $B$. Calculate the length of segment $AB$.

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