
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 curve $C_{1}$ is defined by $\left\{\begin{array}{l}x=\cos t\\y=1+\sin t\end{array}\right.$ (where $t$ is a parameter). Using the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of curve $C_{2}$ is $2\rho \cos \left(\theta -\dfrac{\pi }{3}\right)=3\sqrt {3}$.

1. Find the polar equation of curve $C_{1}$.
2. Given the point $M(2,0)$, the polar equation of the line $l$ is $\theta =\dfrac{\pi }{6}$. The intersection points of $l$ with curve $C_{1}$ are $O$ and $P$, and with curve $C_{2}$ are $Q$. Find the area of $\triangle MPQ$.

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