
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 this sequence does not contain \( d \) consecutive prime numbers for any \( a \) and \( b \).

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