
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 rectangular coordinate system $xOy$, the parametric equation of a line is given by $\begin{cases} x=-1+t\cos\alpha \\ y=1+t\sin\alpha \end{cases}$ (where $t$ is a parameter, and $\alpha \in [0, \pi]$). By establishing a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho=-4\cos\theta$.

1. Write the ordinary equation of line $l$ and the rectangular coordinate equation of curve $C$ when $\alpha = \frac{3\pi}{4}$;
2. Given point $P(-1, 1)$, line $l$ intersects with curve $C$ at two distinct points $A$ and $B$. Find the range of values for $\frac{1}{|PA|} + \frac{1}{|PB|}$.

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