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

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