
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
Evaluate the following sum up to the \(2013^\text{th}\) term:
$$
\left\lfloor\frac{1}{1}\right\rfloor + \left\lfloor\frac{1}{2}\right\rfloor + \left\lfloor\frac{2}{2}\right\rfloor + \left\lfloor\frac{1}{3}\right\rfloor + \left\lfloor\frac{2}{3}\right\rfloor + \left\lfloor\frac{3}{3}\right\rfloor + \left\lfloor\frac{1}{4}\right\rfloor + \left\lfloor\frac{2}{4}\right\rfloor + \left\lfloor\frac{3}{4}\right\rfloor + \left\lfloor\frac{4}{4}\right\rfloor + \left\lfloor\frac{1}{5}\right\rfloor + \cdots 
$$

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