
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 $f(x)= \begin{cases} x^{2}-x & \text{for } x \geq 1, \\ x^{2}-3x+2 & \text{for } x < 1, \end{cases}$ find the range of values for the real number $m$ such that the inequality $f(x)\geq mx$ holds true.

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