
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
Suppose  $(a_n)$ ,  $(b_n)$ ,  $(c_n)$  are arithmetic progressions. Given that  $a_1+b_1+c_1 = 0$  and  $a_2+b_2+c_2 = 1$ , compute  $a_{2014}+b_{2014}+c_{2014}$ .

*Proposed by Evan Chen*

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