
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
Given that in the plane Cartesian coordinate system $xOy$, the parametric equations of the line $l$ are $\left\{\begin{array}{l}x=2-t\\y=1+t\end{array}\right.$ (where $t$ is a parameter), and the equation of curve $C_{1}$ is $x^{2}+y^{2}-x=0$. A polar coordinate system is established with the origin as the pole and the positive x-axis as the polar axis.

(1) Find the polar coordinate equations of the line $l$ and curve $C_{1}$.

(2) The curve $C_{2}:\theta =\alpha \left(\rho  \gt 0,0 \lt \alpha  \lt \dfrac{\pi }{2}\right)$ intersects the line $l$ and curve $C_{1}$ at points $M$ and $N$ respectively. Find the maximum value of $\dfrac{3}{|OM|}+|ON|$.

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