
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 rectangular coordinate system $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x=1+\frac{\sqrt{2}}{2}t \ y=2+\frac{\sqrt{2}}{2}t \end{cases} (t \text{ is the parameter})$, and the polar coordinate system is established with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of curve $C_{2}$ is $\rho=4\sin\theta$.
(I) Write the ordinary equation of line $l$ and the rectangular coordinate equation of curve $C_{2}$.
(II) Line $l$ intersects curve $C_{2}$ at points $A$ and $B$. Find $|AB|$.

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