
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 $a \gt 0$, the function $f(x)=x+\frac{{100}}{x}$ has a minimum value of $m_{1}$ for $x\in \left(0,a\right]$ and a minimum value of $m_{2}$ for $x\in \left[a,+\infty \right)$. If $m_{1}m_{2}=2020$, then the value of $a$ is ______.

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