
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 $x$, $(x-2)(x^2-4x+m)=0$ has three real roots.  
(1) Find the range of values for $m$.  
(2) If these three real roots can exactly be the lengths of the sides of a triangle, find the range of values for $m$.  
(3) If the triangle formed by these three real roots is an isosceles triangle, find the value of $m$ and the area of the triangle.

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