
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
(Polar Coordinates and Parametric Equations)

In the rectangular coordinate system $xOy$, the line $l:\begin{cases}x=t\cos a \\ y=t\sin a\end{cases} (t$ is a parameter, $a\in(0, \dfrac{π}{2}) )$ intersects the circle $C:(x-1)^{2}+(y-2)^{2}=4$ at points $A$, $B$. Establish a polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis.

(1) Write the polar coordinate equations for line $l$ and circle $C$;

(2) Find the maximum value of $\dfrac{1}{|OA|}+ \dfrac{1}{|OB|}$.

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