
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 $f(x)= \frac {\ln x}{1+x}-\ln x$, $f(x)$ reaches its maximum value at $x=x_{0}$. The correct sequence number(s) for the following statements is __________  
$①f(x_{0}) < x_{0}$    
$②f(x_{0})=x_{0}$    
$③f(x_{0}) > x_{0}$    
$④f(x_{0}) < \frac {1}{9}$    
$⑤f(x_{0}) > \frac {1}{9}$．

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