
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
Given the parametric equation of line $l$ as $$\begin{cases} x=t \\ y=t-1 \end{cases}$$ (where $t$ is the parameter), establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of curve $C$ is given by $\rho\sin^2\theta-4\cos\theta=0$ ($\rho\geq0$, $0\leq\theta<2\pi$). If line $l$ intersects curve $C$ at two points $A$ and $B$, find $|AB|=\_\_\_\_\_\_.$

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