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

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