
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 point P is a moving point on the circle $x^2+y^2=2$, and PD is perpendicular to the x-axis with D as the foot of the perpendicular. Also, $\overrightarrow {PD}$$=\sqrt {2}$$\overrightarrow {MD}$.
(1) Find the equation of the trajectory C of the moving point M;
(2) Given the line l: $y=2x+m$ ($m>0$), P is a moving point on the curve represented by trajectory C. If the minimum distance from point P to line l is $\sqrt {5}$, find the value of the real number m.

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