
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
Let the function $f(x)=x^{2}+bx-a\ln x$.

(1) If $x=2$ is an extremum point of the function $f(x)$, and $1$ and $x_{0}$ are two different zeros of the function $f(x)$, with $x_{0} \in (n, n+1), n \in \mathbb{N}$, find $n$.

(2) If for any $b \in [-2, -1]$, there exists $x \in (1, e)$ (where $e$ is the base of the natural logarithm), such that $f(x) < 0$ holds, find the range of the real number $a$.

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