
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 xy, the parametric equation of curve C is given by
$$
\begin{cases}
x = 3\cos\theta \\
y = \sin\theta
\end{cases}
$$
(where $\theta$ is the parameter), and the parametric equation of line l is given by
$$
\begin{cases}
x = a + 4t \\
y = 1 - t
\end{cases}
$$
(where t is the parameter).

1. If $a = -1$, find the coordinates of the intersection points of C and l.
2. If the maximum distance from a point on C to l is $\sqrt {17}$, find $a$.

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