
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 the circle M: $x^2+y^2-2x+a=0$.
1. If $a=-8$, and a tangent line is drawn from point P(4, 5) to circle M, find the equation of this tangent line.
2. If AB is any diameter of circle M, and $\overrightarrow{OA} \cdot \overrightarrow{OB} = -6$ (where O is the origin of coordinates), find the radius of circle M.

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