
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 a quadratic function $y = mx^{2} - 6mx + 4(m$ is a constant).  
$(1)$ Regardless of the value of $m$, the graph of this function will pass through two fixed points, and the coordinates of these two points are ______, ______;  
$(2)$ If points $A(1,a)$, $B(3,b)$, $C(4,c)$ lie on the graph of this function, and when $abc \lt 0$, find the range of values for $m$.

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