
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]


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Elective 4-4: Coordinate System and Parametric Equations

   In the Cartesian coordinate system, the parametric equation of line $l$ is $\begin{cases} & x=-\dfrac{3}{5}t+2 \\ & y=\dfrac{4}{5}t \\ \end{cases}$ ($t$ is the parameter), with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of circle $C$ is $\rho =a\sin \theta (a\ne 0)$.

(1) Find the Cartesian coordinate equation of circle $C$ and the general equation of line $l$;

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

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