
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 all real numbers  $r$ , denote by  $\{r\}$  the fractional part of  $r$ , i.e. the unique real number  $s\in[0,1)$  such that  $r-s$  is an integer.  How many real numbers  $x\in[1,2)$  satisfy the equation  $\left\{x^{2018}\right\} = \left\{x^{2017}\right\}?$ 

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