
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 $f(x)=\begin{cases} \dfrac{1}{|x-1|}, & x\neq 1 \\ 1, & x=1 \end{cases},$ find the sum of the first 10 terms of the arithmetic sequence formed by the 5 distinct roots $x_1, x_2, x_3, x_4, x_5$ of the equation $h(x)={\left[ f(x) \right]}^{2}+bf(x)+\dfrac{1}{2}{b}^{2}-\dfrac{5}{8}$, where $x_1 < x_2 < x_3 < x_4 < x_5$.

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