
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 $\{a_n\}$ with first term $a_1$ and common ratio $q$:
(1) Is the sequence $a_1 + a_2 + a_3$, $a_2 + a_3 + a_4$, $a_3 + a_4 + a_5$, ... a geometric sequence? If so, what are the first term and common ratio?
(2) Is the sequence $\left\{ \frac{1}{a_n} \right\}$ a geometric sequence? If so, what are the first term and common ratio?

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