
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
In the Cartesian coordinate plane $(xOy)$, the curve $y=x^{2}-6x+1$ intersects the coordinate axes at points that lie on circle $C$.
(1) Find the equation of circle $C$;
(2) Given point $A(3,0)$, and point $B$ is a moving point on circle $C$, find the maximum value of $\overrightarrow{OA} \cdot \overrightarrow{OB}$, and find the length of the chord cut by line $OB$ on circle $C$ at this time.

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