
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 a geometric sequence \(\left\{a_{n}\right\}\) with a common ratio greater than 1, where each term is an integer and satisfies \(100 \leqslant a_{n} \leqslant 1000\), what is the maximum number of terms the sequence can have? Write out the sequence \(\left\{a_{n}\right\}\) when the number of terms is maximized (specify each term of the sequence).

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