
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 sets of data arranged in ascending order, set A: $27$, $28$, $37$, $m$, $40$, $50$; set B: $24$, $n$, $34$, $43$, $48$, $52$. If the $30$th percentile and the $50$th percentile of these two sets of data are equal, then $\frac{n}{m}=$____.

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