
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 arithmetic sequences $\{a_n\}$ and $\{b_n\}$, with the sum of the first $n$ terms denoted as $S_n$ and $T_n$, respectively, and the ratio $\frac{a_n}{b_n}$ equals $\frac{3n+21}{n+1}$, find the value of $\frac{S_{15}}{T_{15}}$.

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