
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 sequences $\{a_n\}$ and $\{b_n\}$ are both arithmetic sequences, and $S_n$, $T_n$ are the sums of their first $n$ terms respectively. It is also given that $\frac{S_n}{T_n} = \frac{7n+1}{n+3}$. Find the value of $\frac{a_2+a_5+a_{17}+a_{22}}{b_8+b_{10}+b_{12}+b_{16}}$.

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