
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 integer part $[x]$ of a real number $x$ is the greatest integer $M$ such that $M \leq x$. For example, $[\sqrt{2}]=1, [2]=2, [\pi]=3$. Find all positive real numbers $x$ for which

$$
x[x[x[x]]]<2018
$$

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