
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
For natural numbers \(a > b > 1\), define the sequence \(x_1, x_2, \ldots\) by the formula \(x_n = \frac{a^n - 1}{b^n - 1}\). Find the smallest \(d\) such that for any \(a\) and \(b\), this sequence does not contain \(d\) consecutive terms that are prime numbers.

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