
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
Define a function on the interval $[a, b]$ with length $b-a$, and use $[x]$ to denote the greatest integer less than or equal to $x$. Let $f(x) = [x](x-[x])$ and $g(x) = x-1$. When $0 \leq x \leq 2012$, the length of the solution set interval for the inequality $f(x) \leq g(x)$ is.

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