
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
For an arithmetic sequence {a_n} with the sum of the first n terms denoted as S_n, it is known 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}. Determine the value of S_{2014}.

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