
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
Elective 4-4: Coordinate System and Parametric Equations

Given the parametric equations of line $l$ as $\begin{cases} & x=t\cos \varphi \\ & y=-2+t\sin \varphi \end{cases}$ (where $t$ is the parameter, $0\leqslant \varphi < \pi$), 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 $\rho=1$. Line $l$ intersects $C$ at two distinct points $P_{1}$ and $P_{2}$.

(Ⅰ) Find the range of values for $\varphi$;

(Ⅱ) With $\varphi$ as the parameter, find the parametric equation of the trajectory of the midpoint $M$ of the line segment $P_{1}P_{2}$.

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