
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 $\rho^2 = 4\rho(\cos\theta + \sin\theta) - 3$. If the origin O is taken as the origin of a Cartesian coordinate system and the polar axis lies along the x-axis,  
(Ⅰ) Find the parametric equation of circle C;  
(Ⅱ) In the Cartesian coordinate system, let P(x, y) be a moving point on circle C. Find the maximum value of x + 2y and the Cartesian coordinates of P at that time.

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