
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 functions $f(x)=(a-1)x^{a} (a\in R)$ and $g(x)=|\lg x|$.

(I) If $f(x)$ is a power function, find the value of $a$.

(II) The equation $g(x-1)+f(1)=0$ has two distinct real roots ${x}_{1},{x}_{2}({x}_{1} < {x}_{2})$ in the interval $(1,3)$, find the range of $a+\dfrac{1}{{{x}\_{1}}}+\dfrac{1}{{{x}\_{2}}}$.

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