
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, it is known that the polar equation of circle $C$ is $\rho=2\sqrt{2}\sin(\theta+\frac{\pi}{4})$, and the polar equation of a line is $\rho\cos\theta-\rho\sin\theta+1=0$.

(Ⅰ) Find the area of circle $C$.

(Ⅱ) The line intersects circle $C$ at points $A$ and $B$. Find $|AB|$.

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