
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 that the polar equation of line $l$ is $\rho \sin(\theta + \frac{\pi}{4}) = 2\sqrt{2}$, and the Cartesian equation of circle C is $x^2 + y^2 = 1$,
(1) Find the minimum distance from points on circle C to line $l$;
(2) After applying the scaling transformation $\begin{cases} x' = 2x \\ y' = 3y \end{cases}$ to circle C, resulting in curve $C'$, find the minimum distance from points on curve $C'$ to line $l$.

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