
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 $xOy$, the parametric equations of curve $C$ are $\left\{\begin{array}{l}{x=2+\sqrt{5}\cos\theta,}\\{y=\sqrt{5}\sin\theta}\end{array}\right.$ ($\theta$ is the parameter). The line $l$ with a slope of $60^{\circ}$ passes through the point $P(1,-1)$ and intersects curve $C$ at points $A$ and $B$. <br/>$(1)$ Find the general equation of curve $C$ and a parametric equation of line $l$; <br/>$(2)$ Find the value of $\frac{1}{|PA|}+\frac{1}{|PB|}$.

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