
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 Cartesian coordinate system $xOy$, a line $l$ passing through point $P\left( \frac{\sqrt{3}}{2}, \frac{3}{2}\right)$ at an angle $α$ intersects the curve $C: x^2+y^2=1$ at two distinct points $M$ and $N$.
$(1)$ Write the parametric equation of line $l$;  
$(2)$ Determine the range of the expression $\frac{1}{|PM|}+ \frac{1}{|PN|}$.

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