
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 equations of the line $C$ are $\left\{\begin{array}{l}x=2+t\\y=t+1\end{array}\right.$ (where $t$ is a parameter). The curve $P$ has the polar coordinate equation $\rho ^{2}-4\rho \cos \theta +3=0$ with the origin $O$ of the coordinate system as the pole and the positive x-axis as the polar axis.

(1) Find the general equation of the line $C$ and the rectangular coordinate equation of the curve $P$.

(2) Let the intersection points of the line $C$ and the curve $P$ be $A$ and $B$, find $|AB|$.

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