
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
Given the polar equation of line $l$ is $2\rho\sin(\theta - \frac{\pi}{4}) = \sqrt{2}$, and the polar coordinates of point $A$ are $A(2\sqrt{2}, \frac{7\pi}{4})$, find the distance from point $A$ to line $l$.

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