
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 endpoint B of line segment AB has coordinates (-1, 0), and endpoint A moves on the circle $(x-7)^2+y^2=16$,  
(1) Find the equation of the trajectory of the midpoint M of line segment AB;  
(2) For point C(2, a), if a line that passes through point C and has equal intercepts on both coordinate axes is tangent to the circle, find the value of a and the equation of the tangent line.

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