
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
Given \( x_1 = 3 \) and \( x_n = \frac{x_{n-1}^2 + 2}{2x_{n-1} - 1} \) for \( n = 2, 3, \ldots \), find the general term formula for the sequence \( \{x_n\} \).

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