
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=t\cos φ \\\\ y=-2+t\sin φ\end{cases} (t\\) is a parameter, \\(0\leqslant φ < π )\\), and establishing a polar coordinate system with the origin \\(O\\) as the pole and the positive half-axis of \\(x\\) as the polar axis, the polar equation of curve \\(C\\) is \\(ρ=1\\), line \\(l\\) intersects with \\(C\\) at two different points \\({P}_1,{P}_2 \\).

\\((I)\\) Find the range of \\(φ \\);

\\((II)\\) With \\(φ \\) as the parameter, find the parametric equation of the trajectory of the midpoint of segment \\({P}_1{P}_2 \\).

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