
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 two functions $y=f(x)$ and $y=g(x)$ always satisfy $f(x)g(x) \geqslant 0$ over the same domain, they are called "harmonious functions". Given $f(x)=ax-20$ and $g(x)=\lg\left(\frac{x}{a}\right)$ ($a\in\mathbb{R}$) are harmonious functions over the domain $x\in\mathbb{N}^{*}$, the range of values for $a$ is \_\_\_\_\_\_.

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