
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 plane, the parametric equations of line $l$ are given by $ \begin{cases} x=1+s\,, \\ y=1-s \end{cases}(s \text{ is the parameter}) $, and the parametric equations of curve $C$ are given by $ \begin{cases} x=t+2\,, \\ y=t^2 \end{cases}(t \text{ is the parameter}) $. If line $l$ intersects curve $C$ at points $A$ and $B$, find the length $|AB|$.

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