
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 $x$: $(m-2)x^2+2x+1=0$  (1)  
(1) If equation (1) has real roots, what is the range of real number $m$?  
(2) If $A(1,0)$, $B(2,0)$, and the graph of the function $y=(m-2)x^2+2x+1$ corresponding to equation (1) intersects with line segment AB at only one point, what is the range of real number $m$?

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