
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 power function $f(x) = x^{(2k-1)(3-k)}$ ($k \in \mathbb{Z}$) is an even function and is increasing on $(0, +\infty)$.
1. Find the explicit formula for $f(x)$.
2. Find the range of values for $m$ such that the function $g(x) = f(x) - mx$ is monotonic when $x \in [-1, 1]$.

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