
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
In the arithmetic sequence $\{a\_n\}$, $4a_{12}=-3a_{23} > 0$. Let $b\_n= \frac {a\_n a_{n+1}}{a_{n+2}}$, $S\_n$ is the sum of the first $n$ terms of $\{b\_n\}$, and $S\_{n_0}$ is the maximum term of the sequence $\{S\_n\}$. Find $n\_0$.

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