
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 polar coordinate system, the polar equation of circle $C$ is $\rho =6\cos \theta +8\sin \theta$. Now, establish a Cartesian coordinate system with the pole $O$ as the origin and the positive half-axis of the polar axis as the $x$-axis.  
(Ⅰ) Find the Cartesian coordinate equation of circle $C$;  
(Ⅱ) If the Cartesian coordinates of a moving point $P$ on circle $C$ are $(x,y)$, find the maximum value of $x+y$, and write down the Cartesian coordinates of point $P$ when $x+y$ reaches its maximum value.

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