
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 sequence $\{a_n\}$, where $a_2=6$ and $$\frac {a_{n+1}+a_{n}-1}{a_{n+1}-a_{n}+1}=n.$$  
(1) Find $a_1$, $a_3$, $a_4$;  
(2) Find the general formula for the sequence $\{a_n\}$;  
(3) Calculate $$\lim_{n\rightarrow \infty } \left( \frac {1}{a_{2}-2}+ \frac {1}{a_{3}-3}+…+ \frac {1}{a_{n}-n} \right).$$

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