
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 rectangular coordinate system on a plane, establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the x-axis as the polar axis. The polar coordinates of point A are $( \sqrt {2}，0)$. The distance from point A to line $l：ρsin(θ- \frac {π}{4})=m(m＞0)$ is 3.
(1) Find the value of m and the equation of line l in the rectangular coordinate system;
(2) An moving point M is on the ellipse $C： \frac {y^{2}}{2}+x^{2}=1$. Find the maximum distance from M to line l.

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