
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 equations of the parabola $$
\begin{cases}
x=4t^2\\
y=4t
\end{cases}
$$, if a line with a slope of 1 passes through the focus of the parabola and intersects the parabola at points A and B, find the length of the line segment AB.

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