
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 $a_1$, $a_2$, $a_5$ form a geometric sequence, with $a_3 + a_4 = 12$.
(1) Find $a_1 + a_2 + a_3 + a_4 + a_5$;
(2) Let $b_n = 10 - a_n$, $S_n$ denotes the sum of the first $n$ terms of the sequence ${b_n}$. If $b_1 \neq b_2$, what value of $n$ maximizes $S_n$? What is the maximum value of $S_n$?

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