
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 plane rectangular coordinate system $xOy$, the parameter equation of the line $l$ with an inclination angle $\alpha = 60^{\circ}$ is $\left\{\begin{array}{l}{x=2+t\cos\alpha}\\{y=t\sin\alpha}\end{array}\right.$ (where $t$ is the parameter). Taking the coordinate origin $O$ as the pole, and the non-negative half-axis of the $x$-axis as the polar axis. Establish a polar coordinate system with the same unit length as the rectangular coordinate system. The polar coordinate equation of the curve $C$ in the polar coordinate system is $\rho =\rho \cos ^{2}\theta +4\cos \theta$. <br/>$(1)$ Find the general equation of the line $l$ and the rectangular coordinate equation of the curve $C$; <br/>$(2)$ Let point $P(2,0)$. The line $l$ intersects the curve $C$ at points $A$ and $B$, and the midpoint of chord $AB$ is $D$. Find the value of $\frac{|PD|}{|PA|}+\frac{|PD|}{|PB|}$.

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