
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 $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$, for example, $\lfloor \pi \rfloor = 3$ and $\lfloor -3.2 \rfloor = -4$. Calculate the value of $\lfloor \lg 1 \rfloor + \lfloor \lg 2 \rfloor + \lfloor \lg 3 \rfloor + \ldots + \lfloor \lg 100 \rfloor$.

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