
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 $\{a_n\}$ is an arithmetic sequence and $S_n$ is the sum of the first $n$ terms. It is known that $a_1 + a_3 = 16$ and $S_4 = 28$.
(1) Find the general term formula for the sequence $\{a_n\}$.
(2) For what value of $n$ is $S_n$ maximized, and what is the maximum value?

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