
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 vectors $\overrightarrow{OA}=3i-4j$, $\overrightarrow{OB}=6i-3j$, $\overrightarrow{OC}=(5-m)i-(3+m)j$, where $i$, $j$ are the unit vectors in the positive direction of the $x$ and $y$ axes of the Cartesian coordinate system respectively.  
$(1)$ If points $A$, $B$, $C$ can form a triangle, find the conditions that the real number $m$ must satisfy.  
$(2)$ For any $m\in[1,2]$, the inequality $\overrightarrow{AC}^2 \leqslant -x^2+x+3$ always holds, determine the range of values for $x$.

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