
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

Let $\left\{a_{n}\right\}$ be a sequence with at least four terms such that the sum of the first $n$ terms is $S_{n} = n p a_{n}$ (where $n \in \mathbf{N}_{+}$ and $p$ is a constant), and $a_{1} \neq a_{2}$. What type of sequence is $\left\{a_{n}\right\}$? Provide a justification.

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