
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 the function $f(x) = \{x \cdot \{x\}\}$, where $\{x\}$ denotes the smallest integer not less than $x$, such as $\{1.5\} = 2$, $\{-2.5\} = -2$. When $x \in (0,n]$, $n \in \mathbb{N}^*$, the range of the function $f(x)$ is denoted as $A_n$, and the number of elements in the set $A_n$ is denoted as $a_n$. Then, the value of $\dfrac{1}{a_1} + \dfrac{1}{a_2} + \ldots + \dfrac{1}{a_{2018}} =$ __________.

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