
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 x-y plane of the rectangular coordinate system, the parametric equation of line $l$ is $$\begin{cases} x=t \\ y= \sqrt {3}t+2\end{cases}$$ ($t$ is the parameter), and the parametric equation of curve $C$ is $$\begin{cases} x=cosθ \\ y= \sqrt {3}sinθ\end{cases}$$ ($θ$ is the parameter). Point $P$ is any point on curve $C$. Find the maximum distance from point $P$ to line $l$.

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