
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 inequality $x^2 - 4ax + 3a^2 < 0$ (where $a > 0$), where the solution set is the interval $(x_1,x_2)$, find the minimum value of the expression $x_{1}+x_{2}+ \dfrac {a}{x_{1}x_{2}}$.

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