
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 $g(x)=\ln x+\frac{3}{{4x}}-\frac{1}{4}x-1$, $f(x)=x^{2}-2tx+4$, if for any $x_{1}\in \left(0,2\right)$, there exists $x_{2}\in \left[1,2\right]$, such that $g(x_{1})\geqslant f(x_{2})$, determine the range of real number $t$.

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