
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\}\) whose sums of the first \\(n\\) terms are \\(A_n\\) and \\(B_n\\) respectively, if \\( \dfrac {A_n}{B_n}= \dfrac {7n+45}{n+3}\\), then the number of positive integers that make \\( \dfrac {a_n}{b_n}\\) an integer is \_\_\_\_\_\_.

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