
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
If the function $f(x)$ is increasing in some interval $I$ of its domain $D$, and $\frac{f(x)}{x}$ is decreasing in $I$, then $y=f(x)$ is said to be a "weakly increasing function" in $I$. It is known that the function $h(x)=x^{2}-(b-1)x+b$ is a "weakly increasing function" in $(0,1]$, then the value of the real number $b$ is \_\_\_\_\_\_.

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