
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 $f(x)=\ln x- \frac {1}{4}x+ \frac {3}{4x}-1$ and $g(x)=x^{2}-2bx+4$, if for any $x_{1}\in(0,2)$, there exists $x_{2}\in[1,2]$ such that $f(x_{1})\geqslant g(x_{2})$, then the range of the real number $b$ is \_\_\_\_\_\_.

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