
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 $(xOy)$, the line $l$: $\begin{cases} x=t\cos \alpha \\ y=t\sin \alpha \end{cases}$ ($t$ is a parameter, $\alpha \in (0, \frac{\pi}{2})$) intersects the circle $C$: $(x-1)^2+(y-2)^2=4$ at points $A$ and $B$. Using $O$ as the pole and the positive half of the $x$-axis as the polar axis, establish a polar coordinate system.
(1) Find the polar coordinate equations of line $l$ and circle $C$.
(2) Find the maximum value of $\frac{1}{|OA|} + \frac{1}{|OB|}$.

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