
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 on a plane, a line passes through point $P(0,1)$ with an inclination angle of $\frac{\pi}{6}$. In the polar coordinate system with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis, the equation of curve $C$ is $\rho=4\sin \theta$.

(1) Write the parametric equation of the line and the rectangular coordinate equation of curve $C$.

(2) Suppose the line intersects curve $C$ at points $A$ and $B$. Find the value of $\frac{1}{|PA|}+ \frac{1}{|PB|}$.

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