
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
For the algebraic expression in terms of $x$, $\left(ax-3\right)\left(2x+1\right)-4x^{2}+m$, after simplification, it does not contain the terms $x^{2}$ and constant term. Given that $an+mn=1$, where $an+mn=1$, find the value of $2n^{3}-9n^{2}+8n$.

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