
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 every real number $x$, let $\lfloor x\rfloor$ denote the greatest integer not exceeding $x$, and define \[f(x)=\lfloor x\rfloor(2015^{x-\lfloor x\rfloor}-1).\]  The set of all numbers $x$ such that $1\leq x<2015$ and $f(x)\leq 1$ consists of disjoint intervals. What is the sum of the lengths of these intervals?
A) $0.99$
B) $1$
C) $\log_{2015} 2015$
D) $2$
E) $\frac{\log 2015}{\log 2014}$

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