
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
Given the parametric equation of line $l$ as $\begin{cases} x=-4t+a \\ y=3t-1 \end{cases}(t\in\mathbb{R})$, in the rectangular coordinate system $xOy$, establish a polar coordinate system with point $O$ as the pole and the non-negative half of the $x$-axis as the polar axis. The equation of circle $M$ is given as $(\rho^{2} - 6\rho\sin\theta = -8)$.
(1) Find the rectangular coordinate equation of circle $M$;
(2) If the chord length formed by the intersection of line $l$ and circle $M$ is $\sqrt{3}$, find the value of the real number $a$.

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