
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
In an arithmetic sequence with common difference $d$, denoted as $\{a_n\}$, it is known that $a_1=10$ and that $a_1, 2a_2 + 2, 5a_3$ form a geometric sequence.

(1) Find $d$ and $a_n$.

(2) If $d < 0$, find the sum of the absolute values of the first $n$ terms of the sequence, $|a_1| + |a_2| + |a_3| + \cdots + |a_n|$.

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