
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 $$f(x)= \frac {a+\ln(2x+1)}{2x+1}$$  
(1) If $a=2$, find the extreme values of the function $y=f(x)$;  
(2) If the equation $(2x+1)^2f′(x)=t^3-12t$ always has 3 distinct real roots for $$x\in\left[ \frac {e-1}{2}, \frac {e^{2}-1}{2}\right]$$, find the range of the real number $a$.

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