
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
Find all sets of numbers \( x_{1}, x_{2}, \ldots, x_{n+1} \) such that \( x_{1} = x_{n+1} \) and the following equation holds for all \( k = 1, \ldots, n \):

$$
2 \log_{2} x_{k} \cdot \log_{2} x_{k+1} - \log_{2}^{2} x_{k} = 9
$$

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