
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 function $f\left( x \right)=\left| 1-\frac{1}{x} \right|$.

(1) Does there exist real numbers $a,b\left( a < b \right)$, such that the domain and range of the function $y=f\left( x \right)$ are both $\left[ a,b \right]$? If so, find the values of $a,b$; if not, explain the reason;

(2) If there exist real numbers $a,b\left( a < b \right)$, such that the domain of the function $y=f\left( x \right)$ is $\left[a,b\right]$, and the range is $\left[ma,mb\right]\left(m\neq 0\right)$, find the range of values for the real number $m$.

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