
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
The common ratio of the geometric sequence ${a_n}$ is q, and the eighth term is the arithmetic mean of the second and the fifth terms.
(1) Find the common ratio q;
(2) If the sum of the first n terms of ${a_n}$ is $S_n$, determine whether $S_3$, $S_9$, and $S_6$ form an arithmetic sequence, and explain why.

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