
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 a line $l$ with the equation $ρ\cos θ - ρ\sin θ - 1 = 0 (ρ > 0)$ and a curve $C$ with the parametric equations $ \begin{cases} x = 2\cos α \\ y = 2 + 2\sin α \end{cases} (α \text{ is a parameter})$, where $M$ is a moving point on the curve $C$.
(I) Find the trajectory equation of the midpoint $P$ of the segment $OM$;
(II) Find the minimum distance from the points on curve $C$ to the line $l$.

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