
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 $xOy$, the parametric equation of line $l$ is given by $\begin{cases} x=1- \frac { \sqrt {2}}{2}t \\ y=2+ \frac { \sqrt {2}}{2}t\end{cases}$ (where $t$ is the parameter). Line $l$ intersects the parabola $y^{2}=4x$ at points $A$ and $B$. Find the length of segment $AB$.

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