
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 $xOy$, establish a polar coordinate system with the origin as the pole and the $x$-axis as the polar axis. The polar equation of circle $C$ is $\rho=4$. The parametric equation of the line $l$ is
$$
\begin{cases}
x = a - 2t \\
y = -4t
\end{cases}
$$
where $t$ is the parameter.
(1) Find the general equations of line $l$ and circle $C$.
(2) If line $l$ intersects with circle $C$, determine the range of values for the real number $a$.

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