
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 two sequences $\{a_n\}$ and $\{b_n\}$ satisfying $a_1=1$, $a_2=2$, $b_1=2$, and for any positive integers $i$, $j$, $k$, $l$, when $i+j=k+l$, it holds that $a_i+b_j=a_k+b_l$, calculate the value of $$\frac {1}{2013} \sum\limits_{i=1}^{2013}(a_{i}+b_{i})$$

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