
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 $[x]$ denote the greatest integer not exceeding $x$, and let $\{x\} = x - [x]$. Find the value of the sum $\left\{\frac{2012+1}{5}\right\} + \left\{\frac{2012+2}{5}\right\} + \left\{\frac{2012+3}{5}\right\} + \cdots + \left\{\frac{2012+2012}{5}\right\}$.

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