
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 the function $f(x)=\ln \frac {ex}{e-x}$, if $f( \frac {e}{2013})+f( \frac {2e}{2013})+…+f( \frac {2012e}{2013})=503(a+b)$, calculate the minimum value of $a^{2}+b^{2}$.

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