
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 $f(x) = x^{-2m^2 + m + 3}$ where $m \in \mathbb{Z}$, it is known to be an even function and increases on the interval $(0, +\infty)$.

(1) Find the expression for $f(x)$;

(2) If $g(x) = \log_a[f(x) - ax]$ where $a > 0$ and $a \neq 1$ is an increasing function on the interval $[2, 3]$, find the range of values for the real number $a$.

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