
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 $$\begin{cases} x=t\cos\phi \\ y=-2+t\sin\phi \end{cases}$$ (where $t$ is a parameter, $0 \leq \phi < \pi$), 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 $P_2$.  
(1) Find the range of $\phi$;  
(2) With $\phi$ as the parameter, find the parametric equation for the trajectory of the midpoint of segment $P_1P_2$.

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