
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
(1) In the arithmetic sequence $\{a_n\}$, $a_8=6$, $a_{10}=0$, find the general formula for $\{a_n\}$ and the sum of the first $n$ terms $S_n$, and indicate the value of $n$ when $S_n$ reaches its maximum value;  
(2) In the geometric sequence $\{a_n\}$, $a_{1}= \frac {1}{2}$, $a_{4}=4$, find the general formula for $\{a_n\}$ and the sum of the first $n$ terms $S_n$.

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