
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 $\{a_n\}$ and $\{b_n\}$, the sums of the first $n$ terms are $A_n$ and $B_n$ respectively, and $\frac{A_n}{B_n} = \frac{6n+54}{n+5}$. Find the number of positive integers $n$ for which $\frac{a_n}{b_n}$ is an integer.

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