
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
The function f(x) is defined on R as follows: $$\begin{cases} \frac {1}{|x-1|}, x\neq1 \\ 1, x=1\end{cases}$$ If the function h(x) = f^2(x) + bf(x) + $\frac {1}{2}$ has 5 distinct zeros $x\_1$, $x\_2$, $x\_3$, $x\_4$, $x\_5$, then the value of $x\_1^2+x\_2^2+x\_3^2+x\_4^2+x\_5^2$ is \_\_\_\_\_\_.

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