
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, the line $l$ and the curve $C$ are given by the following parametric equations respectively: 

$$
l: \begin{cases} 
x=1+s \\ 
y=1-s 
\end{cases} \quad (s \text{ is the parameter}),
$$

and 

$$
C: \begin{cases} 
x=t+2 \\ 
y=t^{2} 
\end{cases} \quad (t \text{ is the parameter}).
$$

If $l$ intersects $C$ at points $A$ and $B$, then the length of the line segment $AB$ is __________.

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