
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 $f(x)=\ln x+ax^{2}$,
(1) Let $m(x)=f′(x)$. If $m′(1)=3$, find the value of the real number $a$;
(2) Given the function $g(x)=f(x)-ax^{2}+ax$. If $g(x)$ is monotonically increasing on $(0,+∞)$, find the value of the real number $a$.

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