
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 $\begin{cases} x=-1+ \frac { \sqrt {2}}{2}t \\ y=2+ \frac { \sqrt {2}}{2}t \end{cases}$ ($t$ is the parameter), and the parametric equation of curve $C$ is given by $\begin{cases} x=4\cos \theta \\ y=\cos 2\theta \end{cases}$ ($\theta$ is the parameter).
(1) Convert the parametric equation of curve $C$ into a standard form;
(2) Find the maximum distance from a point on curve $C$ to line $l$.

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