
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 ${a_n}$ with the sum of its first $n$ terms as $S_n$, $a_1 = -8$, and $(3n-5)a_{n+1} = (3n-2)a_n - 9n^2 + 2ln -10$, calculate the maximum value of $S_n - S_m$ when $n,m \in \mathbb{N}^*, n > m$.

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