
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 coordinate equation of line $l$ as $2\rho \sin (\theta - \frac{\pi }{4})=\sqrt{2}$, and point $A$ with polar coordinates $A\left( 2\sqrt{2},\frac{7\pi }{4} \right)$, find the distance between point $A$ and line $l$.

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