
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
Suppose $4-4$: Coordinate Systems and Parametric Equations

In the rectangular coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases} & x=-\frac{3}{5}t+2 \\ & y=\frac{4}{5}t \\ \end{cases}$ ($t$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of circle $C$ is $\rho =a\sin \theta$.

(1) If $a=2$, find the rectangular equation of circle $C$ and the general equation of line $l$;

(2) If the chord length of circle $C$ intercepted by line $l$ is $\sqrt{3}$ times the radius length of circle $C$, find the value of $a$.

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