
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 pole is at the origin O of the Cartesian coordinate system, and the polar axis coincides with the positive half-axis of the x-axis. The unit lengths of both coordinate systems are the same. It is known that the polar equation of the curve is $\rho=2\cos\theta+2\sin\theta$, and the parametric equation of line $l$ is $$\begin{cases} x=2-t \\ y=-1+t\end{cases}$$ (where $t$ is the parameter).
(Ⅰ) Convert the parametric equation of line $l$ into a standard equation, and convert the polar equation of curve $C$ into a Cartesian coordinate equation;
(Ⅱ) Let $f(d)$ be the number of points on curve $C$ that are at a distance $d$ from line $l$. Find the expression for $f(d)$.

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