
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 point is $(4, \frac{\pi}{4})$, and the equation of the line is $\rho \sin(\theta + \frac{\pi}{4}) = 1$.
(1) Find the Cartesian coordinates of the point $(4, \frac{\pi}{4})$ and the standard form of the line's equation.
(2) Calculate the distance from the point $(4, \frac{\pi}{4})$ to the line $\rho \sin(\theta + \frac{\pi}{4}) = 1$.

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