
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 sets $A=\{x|x=2n-1,n\in\mathbb{N}^*\}$ and $B=\{x|x=2^n,n\in\mathbb{N}^*\}$. Arrange all elements of $A\cup B$ in ascending order to form a sequence $\{a_n\}$. Let $S_n$ denote the sum of the first $n$ terms of the sequence $\{a_n\}$. Find the smallest value of $n$ such that $S_n > 12a_{n+1}$.

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