
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
The equation of curve C is given by the parametric equations
$$
\begin{cases} 
x=8t^{2} \\
y=8t
\end{cases}
\quad (t \text{ is the parameter})
$$
A line with an inclination angle of $\frac{\pi}{4}$ passes through point F(2, 0) and intersects curve C at points A and B. Find the length of segment AB.

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