
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 $f(x)=\ln x-ax-1$ $(a\in \mathbb{R})$, $g(x)=xf(x)+ \frac {1}{2}x^{2}+2x$.

(Ⅰ) Find the monotonic intervals of $f(x)$;

(Ⅱ) When $a=1$, if the function $g(x)$ has a unique extreme point in the interval $(m,m+1)$ $(m\in \mathbb{Z})$, find the value of $m$.

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