
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 the equation about $x$, $(x-1)(x^2-3x+m)=0$, where $m$ is a real number.  
(1) When $m=4$, find the roots of the equation;  
(2) If exactly two of the three real roots of the equation are equal, find the value of $m$;  
(3) If the three real roots of the equation can exactly form the side lengths of a triangle, find the range of values for $m$.

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