
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 $f(x) = (a-1)x^a$ ($a \in \mathbb{R}$), $g(x) = |\log_{10}x|$.  
(I) If $f(x)$ is a power function, find the value of $a$ and its decreasing interval;  
(II) The equation $g(x-1) + f(1) = 0$ has two different real roots $x_1$, $x_2$ ($x_1 < x_2$) in the interval $(1, 3)$. Find the range of values for $a + \frac{1}{x_1} + \frac{1}{x_2}$.

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