
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
The given arithmetic sequences $\{a_{n}\}$ and $\{b_{n}\}$ have respective sums of the first $n$ terms, denoted by $S_{n}$ and $T_{n}$. The ratio $\frac{S_{n}}{T_{n}} = \frac{3n + 1}{n + 3}$. Determine the value of $\frac{a_{2} + a_{20}}{b_{7} + b_{15}}$.

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