
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
For any real number $x$, $\lfloor x \rfloor$ represents the integer part of $x$, meaning $\lfloor x \rfloor$ is the greatest integer that does not exceed $x$. This function $\lfloor x \rfloor$ is called the "floor function". Find the sum $\lfloor \lg 1 \rfloor + \lfloor \lg 2 \rfloor + \lfloor \lg 3 \rfloor + \lfloor \lg 4 \rfloor + \ldots + \lfloor \lg 2013 \rfloor$.

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