
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 with the origin as the pole and the positive x-axis as the polar axis, the polar equation of circle C is: $\rho^2 - 4\sqrt{2}\rho\cos(\theta - \frac{\pi}{4}) + 7 = 0$.
(Ⅰ) Convert the polar equation into a Cartesian equation;
(Ⅱ) If point P $(x, y)$ is on circle C, find the range of values for $x + \sqrt{3}y$.

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