
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
Let $P$ and $Q$ be points on the circle $(x-0)^2+(y-6)^2=2$ and the ellipse $\frac{x^2}{10}+y^2=1$, respectively. What is the maximum distance between $P$ and $Q$?
A) $5\sqrt{2}$
B) $\sqrt{46}+\sqrt{2}$
C) $7+\sqrt{2}$
D) $6\sqrt{2}$

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