
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 equation of line $l$ is $$\begin{cases} x=1+t\cos\theta \\ y=t\sin\theta\end{cases}$$ (where $t$ is the parameter, $0\leq\theta<\pi$). Taking the origin as the pole and the non-negative half-axis of $x$ as the polar axis, we establish a polar coordinate system. The polar equation of circle $C$ is $\rho=-4\cos\alpha$. The distance from the center of circle $C$ to line $l$ is $\frac{3}{2}$.  
(1) Find the value of $\theta$;  
(2) Given $P(1,0)$, if line $l$ intersects circle $C$ 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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