
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
The parametric equations for curve $C_1$ are $$\begin{cases} \left.\begin{matrix}x=3\cos\theta \\ y=3\sin\theta\end{matrix}\right.\end{cases}$$ (where $\theta$ is the parameter), and the polar equation for curve $C_2$ is $\rho^2+6\cos\theta-2\rho\sin\theta+6=0$. Determine the number of common tangents to the curves $C_1$ and $C_2$.

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