
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 $f(x)=6\ln x+x^2-8x$, and $g(x)= \frac {p}{x}+x^{2}$ ($p\in \mathbb{R}$).  
(1) Find the interval where the function $f(x)$ is monotonically increasing;  
(2) If there exists at least one point $x_0$ in the interval $[1, e]$ such that $f(x_0) > g(x_0)$, find the range of the real number $p$.

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