
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
Given a function $f(x)$ defined on $\mathbb{R}$ that satisfies the equation $f(x)+f(1-x)=1$ for all $x$, and for $x \geqslant 0$ the relation $f\left(\dfrac{x}{3}\right)=\dfrac{1}{2}f(x)$ holds, and for $0 \leqslant x_1 < x_2 \leqslant 1$, $f(x_1)\leqslant f(x_2)$, find the value of $f\left(\dfrac{1}{2018}\right)$.

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