
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 that \( n \) and \( k \) are positive integers, and the sequence \( a_1, a_2, \cdots, a_{k+1} \) is a geometric sequence such that \( n^k \leq a_i \leq (n+1)^k \) for \( i = 1, 2, \cdots, k+1 \), find all such sequences.

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