
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 q < 1, and the sum of the first n terms is S<sub>n</sub>. If a<sub>2</sub> = 2 and S<sub>3</sub> = 7:

1. Find the general term formula for {a<sub>n</sub>}.
2. Let m ∈ Z. If S<sub>n</sub> < m always holds true, find the minimum value of m.

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