
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 solution set of the inequality $-x^{2}+6ax-3a^{2}\geqslant 0$ with respect to $x$ is $[x_{1}$,$x_{2}]$, where the constant $a \gt 0$, then the minimum value of ${x_1}+{x_2}+\frac{{3a}}{{{x_1}{x_2}}}$ is ______.

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