
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 equation of line $l$ is given by 
$$
\begin{cases} 
x=-8+t \\
y=\frac{t}{2} 
\end{cases}
(t \text{ is the parameter}),
$$
and the parametric equations of the curve $C$ are 
$$
\begin{cases} 
x=2s^{2} \\
y=2\sqrt{2}s 
\end{cases}
(s \text{ is the parameter}).
$$
Let $P$ be a moving point on curve $C$. Find the minimum distance from point $P$ to line $l$.

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