
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
For the quadratic function $y=mx^{2}-(4m+1)x+3m+3$ where $m \lt 0$, the following statements are made:<br/>① When $x \gt 2$, $y$ decreases as $x$ increases;<br/>② Regardless of the value of $m$, the graph of the function must pass through the points $(1,2)$ and $(3,0)$;<br/>③ The distance between the two intersection points of the graph of this quadratic function and the $x$-axis is less than $2$;<br/>④ The minimum value of the ordinate of the vertex of the graph of this function is $2$;<br/>The correct statements are ____. (Only fill in the numbers)

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