
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, with the origin as the pole and the positive x-axis as the polar axis, a polar coordinate system is established. The equation of the curve C<sub>1</sub> is given by $\rho=2\cos\theta+2\sin\theta$, and the parametric equation of the line C<sub>2</sub> is
$$
\begin{cases}
x=-1+t \\
y=-1-t
\end{cases}
$$
where $t$ is the parameter.

(Ⅰ) Convert the equation of C<sub>1</sub> into a rectangular coordinate equation.
(Ⅱ) Let P be a moving point on C<sub>1</sub>. Find the maximum and minimum distance from P to the line C<sub>2</sub>.

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