
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 in terms of $x$, $y=x^{2}-6x+2m-1$,  
$(1)$ For what value of $m$ does the function not intersect the $x$-axis?  
$(2)$ When $m=-3$, find the coordinates of the intersection points of the quadratic function with the coordinate axes.

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