
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<sub>n</sub>} is a geometric sequence with a common ratio not equal to 1, S<sub>n</sub> represents the sum of its first n terms, a<sub>2</sub> = 2, and 16a<sub>1</sub>, 9a<sub>4</sub>, 2a<sub>7</sub> form an arithmetic sequence, find the value of S<sub>3</sub>.

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