
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 \(\{x_{n}\}\), \(x_{1} = 3\), \(x_{2} = 2\), and \(x_{n} = \frac{x_{n-2} x_{n-1}}{2 x_{n-2} - x_{n-1}} \) (for \( n \geq 3, n \in \mathbf{N} \)), find the general term formula of the sequence \(\{x_{n}\}\).

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