
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 in the rectangular coordinate system (with $O$ as the origin), $\overrightarrow{OA}=(2,5)$, $\overrightarrow{OB}=(3,1)$, $\overrightarrow{OC}=(x,3)$.
(I) If $A$, $B$, and $C$ can form a triangle, find the range of values for $x$;
(II) When $x=6$, there exists a point $M$ on the line $OC$ such that $\overrightarrow{MA} \perp \overrightarrow{MB}$, find the coordinates of point $M$.

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