
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 $f(x)=\ln x-a^{2}x^{2}+ax$, where $a\in\mathbb{R}$, and $a\neq 0$.

$(1)$ If $a > 0$, the function $f(x)$ is decreasing on the interval $[1,+\infty)$. Find the range of the real number $a$.

$(2)$ Let the function $g(x)=(3a+1)x-(a^{2}+a)x^{2}$. If $x > 1$, $f(x) < g(x)$ always holds. Find the range of $a$.

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