
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 the arithmetic sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$, let $A_{n}=a_{1}+a_{2}+\cdots+a_{n}$ and $B_{n}=b_{1}+b_{2}+\cdots+b_{n}$. For all $n \in \mathbf{N}^{*}$, if $\frac{A_{n}}{B_{n}}=\frac{3n+5}{5n+3}$, determine the value of $\frac{a_{10}}{b_{6}}$.

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