
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 a sequence $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, $a_1=15$, and it satisfies $\frac{a_{n+1}}{2n-3} = \frac{a_n}{2n-5}+1$, knowing $n$, $m\in\mathbb{N}$, and $n > m$, find the minimum value of $S_n - S_m$.

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