
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
Suppose the sequence ${a_n} (n \in \mathbb{N}^*)$ is an arithmetic sequence, then the sequence $b_n = \frac{a_1 + a_2 + ... + a_n}{n} (n \in \mathbb{N}^*)$ is also an arithmetic sequence. By analogy, if the sequence ${c_n}$ is a geometric sequence with $c_n > 0$, then the sequence $d_n =$ _______ $(n \in \mathbb{N}^*)$ is also a geometric sequence.

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