
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 the first term of the sequence ${a_n}$ is 1, and $a_{n+1} - a_n = a_n - a_{n-1}$ holds for all positive integers $n$ greater than 1, and $S_3 + S_5 = 2a_9$, find the value of $a_6 + a_{12}$.

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