
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
Let {a<sub>n</sub>} be a geometric sequence satisfying a<sub>1</sub> + a<sub>2</sub> = 4 and a<sub>3</sub> - a<sub>1</sub> = 8.  
(1) Find the general formula for {a<sub>n</sub>}.  
(2) Let S<sub>n</sub> be the sum of the first n terms of the sequence {log<sub>3</sub>a<sub>n</sub>}. If S<sub>m</sub> + S<sub>m+1</sub> = S<sub>m+3</sub>, find the value of m.

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