
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 $f(x)=\ln x+x^{2}$.
(1) If the function $g(x)=f(x)-ax$ is an increasing function in its domain, find the range of values for the real number $a$.
(2) Under the condition of (1) and $a > 1$, let $h(x)=e^{3x}-3ae^{x}$, $x\in[0,\ln 2]$, find the minimum value of $h(x)$.

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