
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, it is known that the line $l$ with parameter $s$: 
$$
\begin{cases} 
x = 1 + s \\ 
y = 2 - s
\end{cases}
$$
intersects with the curve $C$ with parameter $t$: 
$$
\begin{cases}
x = t + 3 \\
y = t^{2}
\end{cases}
$$
at points $A$ and $B$. Find the length of segment $AB$.

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