
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
The sequence $\{{a_{n}}\}$ satisfies ${a_{n+2}}-2{a_{n+1}}+{a_{n}}=0(n\in {N^{*}})$, where ${a_{1}}=8$ and ${a_{4}}=2$.

(1) Find the general term formula for the sequence $\{{a_{n}}\}$.
(2) Calculate the sum $|{a_{1}}|+|{a_{2}}|+...+|{a_{15}}|$.

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