
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 \(\{a_{n} \mid n \geq 1\}\) and \(\{b_{n} \mid n \geq 1\}\), let \(A_{n} = a_{1} + \cdots + a_{n}\) and \(B_{n} = b_{1} + \cdots + b_{n}\). If for all \(n \geq 1\), \(\frac{A_{n}}{B_{n}} = \frac{4n + 1}{8n + 3}\), find \(\frac{a_{10}}{b_{10}}, \frac{a_{10}}{a_{7}}, \frac{b_{10}}{b_{7}}\).

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