
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, two points A(3, $\frac{\pi}{4}$) and B($\sqrt{2}$, $\frac{\pi}{2}$) are given. The equation of line 1 is $\rho \sin(\theta + \frac{\pi}{4}) = 3$.
(1) Find the distance between points A and B.
(2) Find the distance from point B to line 1.

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