
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 polar coordinates, it is known that point $A$ has the polar coordinates $(2\sqrt{2},\frac{\pi}{4})$, and the polar equation of circle $E$ is $\rho=4\sin\theta$. Then, the distance between the center of circle $E$ and point $A$, denoted as $d$, is $\boxed{2}$.

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