
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 \(xoy\), the parametric equations for the line \(l\) are given by
\[
\begin{cases}
x=a+2t \\
y=1-t
\end{cases}
\]
where \(t\) is the parameter. With the origin as the pole and the positive \(x\)-axis as the polar axis, the polar equation for the curve \(C\) is \(\rho=2\).
1. If \(a=-2\), find the coordinates of the intersection point(s) of \(C\) and \(l\).
2. If the maximum distance from a point on \(C\) to the line \(l\) is \(2 \sqrt{5}\), find the value of \(a\).

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