
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 $M$: $(x-a)^2+(y-4)^2=r^2$ $(r > 0)$ passes through points $O(0,0)$ and $A(6,0)$.

(I) Find the values of $a$ and $r$.
(II) If circle $M$ intercepts a chord on line $4x+3y+m=0$ with a chord length of $6$, find the value of $m$.

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