
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 sequence \(\left\{a_{n}\right\}\), \(a_{1} = -1\), \(a_{2} = 1\), \(a_{3} = -2\). Given that for all \(n \in \mathbf{N}_{+}\), \(a_{n} a_{n+1} a_{n+2} a_{n+3} = a_{n} + a_{n+1} + a_{n+2} + a_{n+3}\), and \(a_{n+1} a_{n+2} a_{n+3} \neq 1\), find the sum of the first 4321 terms of the sequence \(S_{4321}\).

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