
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 the sequence ${a_n}$ that satisfies the condition $2a_{n+1} = a_n + a_{n+2}$ for any $n \in \mathbb{N}^*$, and $a_1 + a_4 = 41$, $a_3 + a_7 = 26$,
(1) Find the general term formula $a_n$.
(2) Calculate the value of $|a_1| + |a_3| + |a_5| + ... + |a_{19}|$.

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