
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
(1) Given $$\lim_{x\to \infty} \left( \frac {2n^{2}}{n+2}-na\right)=b$$, find the values of $a$ and $b$.  
(2) Given $$\lim_{x\to \infty} \frac {3^{n}}{3^{n+1}+(a+1)^{n}}= \frac {1}{3}$$, find the range of values for $a$.

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