
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
The function $y=[x]$ is called the "floor function", where the symbol $[x]$ represents the integer part of $x$, that is, $[x]$ is the largest integer not exceeding $x$. For example, $[2]=2$; $[2.1]=2$; $[-2.2]=-3$. Then, the value of $[\lg1]+[\lg2]+[\lg3]+\ldots+[\lg2016]$ is.

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