
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 $f\left( x \right)=\ln x-{a}^{2}{x}^{2}+ax,a\in R$, and $a\ne 0$.

(1) If the function $f\left( x \right)$ is a decreasing function in the interval $\left[ 1,+\infty \right)$, find the range of values for the real number $a$.

(2) Given the function $g\left( x \right)=\left( 3a+1 \right)x-\left( {a}^{2}+a \right){x}^{2}$, when $x > 1$, $f\left( x \right) < g\left( x \right)$ always holds true. Find the range of values for $a$.

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