
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 distance from point A ($$\sqrt{2}$$, 0) to the line $l$: $\rho\sin(\theta - \frac{\pi}{4}) = m$ ($m > 0$) is 3.  
(1) Find the value of $m$.  
(2) Let $P$ be a moving point on line $l$, and point $Q$ is on the line segment $OP$, satisfying $|\overrightarrow{OP}| \cdot |\overrightarrow{OQ}| = 1$, find the equation of the trajectory of point $Q$.

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