
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 $$\frac {x^{2}}{9}+y^{2}=1.$$ In a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, the polar equation of curve $C_2$ is $\rho^{2}-8\rho\sin\theta+15=0.$  
(Ⅰ) Write the parametric equation of $C_1$ and the Cartesian equation of $C_2$;  
(Ⅱ) Let point $P$ be on $C_1$ and point $Q$ be on $C_2$, find the maximum value of $|PQ|$.

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