
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 a sequence $\{a_n\}$ whose sum of the first $n$ terms is $S_n=3n^2+8n$, and a sequence $\{b_n\}$ is an arithmetic sequence, and $a_n=b_n+b_{n+1}$  
$(1)$ Find the general formula for sequences $\{a_n\}$, $\{b_n\}$, $a_n$, $b_n$  
$(2)$ Let $c_n= \frac {(a_n+1)^{n+1}}{(b_n+2)^n}$, and $\lambda > \frac {c_{n+1}}{c_n}$ holds for any $n\in N^*$, find the range of the real number $\lambda$.

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