
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 sums of the first $n$ terms of the arithmetic sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ are $S_{n}$ and $T_{n}$, respectively. If for any positive integer $n$, the following holds:
$$
\frac{S_{n}}{T_{n}}=\frac{5 n-3}{2 n+1}, 
$$
then find the value of $\frac{a_{20}}{b_{7}}$.


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