
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 given by $\begin{cases} x=t\cos \alpha \\ y=t\sin \alpha \end{cases}(t$ is a parameter, $0 < \alpha < \pi )$, and curve $C$'s polar coordinate equation is $\rho = \frac{p}{1-\cos \theta }(p > 0)$.

(1) Write the polar coordinate equation of line $l$ and the Cartesian coordinate equation of curve $C$;

(2) If line $l$ intersects with curve $C$ at points $A$ and $B$, find the value of $\frac{1}{|OA|}+\frac{1}{|OB|}$.

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