
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 coordinates of point A are $$( \frac {3}{2}, 0)$$, and point B moves on the circle O: $x^2+y^2=7$, a line segment BM is drawn with point B as one endpoint such that point A is the midpoint of line segment BM.  
(1) Find the equation of the trajectory C of the endpoint M of line segment BM;  
(2) It is known that the line $x+y-m=0$ intersects the trajectory C at two points P and Q, and the circle with PQ as its diameter passes through the origin O. Find the value of the real number m.

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