
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
Let \(A_{n}\) and \(B_{n}\) be the sums of the first \(n\) terms of two arithmetic sequences \(\{a_n\}\) and \(\{b_n\}\), respectively. If \(\frac{A_{n}}{B_{n}} = \frac{5n - 3}{n + 9}\), find the value of \(\frac{a_6}{b_3}\).

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