
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
Find the sum of the first 2014 terms of the arithmetic sequence ${a_n}$ given that $(a_2-1)^3 + 2014(a_2-1) = \sin{\frac{2011\pi}{3}}$ and $(a_{2013}-1)^3 + 2014(a_{2013}-1) = \cos{\frac{2011\pi}{6}}$.

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