
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 geometric sequences $\{a_n\}$ and $\{b_n\}$, their respective sums of the first $n$ terms are $S_n$ and $T_n$. If for any $n\in \mathbb{N}^*$, it always holds that $\frac{S_n}{T_n}=\frac{3^n+1}{4}$, then $\frac{a_3}{b_3}=$ ______ .

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