
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 $\left\lbrack x \right\rbrack$ denote the greatest integer less than or equal to $x$, such as $\left\lbrack \pi \right\rbrack=3$, $\left\lbrack -3.2 \right\rbrack=-4$. Then, find the value of $\left\lbrack \lg 1 \right\rbrack+\left\lbrack \lg 2 \right\rbrack+\left\lbrack \lg 3 \right\rbrack+⋯+\left\lbrack \lg 100 \right\rbrack$.

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