
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
A math interest group is researching the quadratic function $y=mx^2-2mx+3$ (where $m \neq 0$) and has noticed that, as the value of $m$ changes, both the shape and position of the graph of the quadratic function change. However, the graph always passes through two fixed points. Please provide the coordinates of these two fixed points.

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