
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 the sequence \\(\{a_n\}\) is a geometric sequence.

\\((1)\\) If \\(a_1+a_2+a_3=21\\) and \\(a_1a_2a_3=216\\), find \\(a_n\\);

\\((2)\\) If \\(a_3a_5=18\\) and \\(a_4a_8=72\\), find the common ratio \\(q\\).

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