
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
Given the parametric equation of line $l$ as $$\begin{cases} x=4-2t \\ y=t-2 \end{cases}$$ (where $t$ is the parameter), and $P$ is any point on the ellipse $$\frac {x^{2}}{4}+y^{2}=1$$, find the maximum distance from point $P$ to line $l$.

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