
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 $f(x)=\max\{{x}^{2},\frac{1}{x}\}$, where $\max\{a,b\}=\left\{\begin{array}{l}a,a\geqslant b\\ b,a＜b\end{array}\right.$, determine the range of positive real number $a$ such that $f\left(a\right) \geqslant 4$.

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