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

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