
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 $f(x) = x^2 - 2x + 2$,
1. Find the intervals where $f(x)$ is monotonic.
2. Find the maximum and minimum values of $f(x)$ on the interval $[\frac{1}{2}, 3]$.
3. If $g(x) = f(x) - mx$ is monotonic on the interval $[2, 4]$, determine the range of values for $m$.

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