
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 $\begin{cases}x=t \\ y=a-t\end{cases}$ (where $t$ is the parameter). With the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equation of circle $C$ is $\rho =4\cos \theta$.

(Ⅰ) Find the general equation of line $l$ and circle $C$;

(Ⅱ) If the ratio of the arc lengths divided by line $l$ on circle $C$ is $3:1$, find the value of the real number $a$.

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