
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 equation of curve $C_{1}$ is $x^{2}+\left(y-1\right)^{2}=1$. Point $P$ is a moving point on curve $C_{1}$, and $\overrightarrow{OQ}=2\overrightarrow{OP}$, where point $Q$ traces out curve $C_{2}$. Establish a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis.<br/>$(Ⅰ)$ Find the polar coordinate equations of curves $C_{1}$ and $C_{2}$;<br/>$(Ⅱ)$ The polar coordinate equation of curve $C_{3}$ is ${\rho^2}=\frac{2}{{1+{{sin}^2}θ}}$. Point $M$ is a moving point on curve $C_{3}$. Find the maximum value of $|MQ|$.

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