
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 two sequences $\{a_n\}$ and $\{b_n\}$ satisfying $a_n=2b_n+3$ ($n\in\mathbb{N}^*$), if the sum of the first $n$ terms of $\{b_n\}$ is $S_n= \frac {3}{2}(3^{n}-1)$ and $\lambda a_n > b_n+36(n-3)+3\lambda$ holds for all $n\in\mathbb{N}^*$, then the range of the real number $\lambda$ is \_\_\_\_\_\_.

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