
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 parametric equation of curve $C_1$ is: 
$$
\begin{cases} 
x=3\cos\alpha \\
y=3+3\sin\alpha 
\end{cases}
$$
where $\alpha$ is the parameter. Let $M$ be a moving point on $C_1$, and point $P$ satisfies $\overrightarrow{OP} = 2\overrightarrow{OM}$. The trajectory of point $P$ is curve $C_2$.

(1) Find the parametric equation of $C_2$.

(2) In the polar coordinate system with $O$ as the pole and the positive half-axis of $x$ as the polar axis, the ray $\theta= \frac{\pi}{3}$ intersects $C_1$ at point $A$ (different from the pole) and intersects $C_2$ at point $B$ (different from the pole). Find $|AB|$.

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