
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 $f(x)=x|x-2a|+a^{2}-3a$, if the function $f(x)$ has three distinct zeros $x_{1}$, $x_{2}$, $x_{3}$, and $x_{1} \lt x_{2} \lt x_{3}$, then the range of $a$ is ______, and the range of $\frac{1}{{{x_1}}}+\frac{1}{{{x_2}}}+\frac{1}{{{x_3}}}$ is ______.

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