
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
Let $\{a_n\}$ be a geometric sequence with the first term as 1. If $\left\{ \frac {1}{2a_{n}+a_{n+1}}\right\}$ is an arithmetic sequence, then find the value of $( \frac {1}{2a_{1}}+ \frac {1}{a_{2}})+( \frac {1}{2a_{2}}+ \frac {1}{a_{3}})+…+( \frac {1}{2a_{2012}}+ \frac {1}{a_{2013}})$.

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