
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 the endpoint B of segment AB is (-1, 0), and the endpoint A moves on the circle (x-7)²+y²=16,
1. Find the trajectory equation of the midpoint M of segment AB;
2. Suppose point C is (2, a) (a>0), and the line passing through point C intercepts equal lengths on the two coordinate axes and is tangent to the curve corresponding to the trajectory equation of point M. Find the value of a and the slope-intercept form of the tangent line.

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