
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 sequences $\{a_n\}$ and $\{b_n\}$ satisfy $a_{n+1}=3a_n$, $b_n=b_{n+1}-1$, $b_6=a_1=3$, if $(2\lambda-1)a_n > 36b_n$ 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}
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