
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 $\begin{cases} x=1+\frac{\sqrt{2}}{2}t \\ y=2+\frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is $\rho=4\sin \theta$.

(1) Write the general equation of line $l$ and the rectangular coordinate equation of curve $C$;

(2) Line $l$ intersects curve $C$ at points $A$ and $B$. Calculate $|AB|$.

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