
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 $f(x) = (m^2 - 3m + 3)x^{m+1}$ is an even function, and $g(x) = \log_a[f(x) - ax]$ ($a > 0$ and $a \neq 1$).
(Ⅰ) Find the explicit formula for $f(x)$;
(Ⅱ) If $g(x)$ is an increasing function in the interval $(2, 3)$, find the range of the real number $a$.

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