
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
The geometric sequence $\left\{a_{n}\right\}$ has the first term $a_{1}=1536$, and common ratio $q=-\frac{1}{2}$. Let $\Pi_{n}$ denote the product of its first $n$ terms $\left(n \in \mathbf{N}^{*}\right)$. Find the value of $n$ that maximizes $\Pi_{n}\$.

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