
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 a function $y=f(x)$ where $x \in I$. If there exists a constant $M$ such that for any $x_1 \in I$, there is a unique $x_2 \in I$ satisfying $\dfrac{f(x_{1}) + f(x_{2})}{2} = M$, then $M$ is called the "average value" of the function $f(x)$ on $I$. Given $f(x) = \log_{2}x$ for $x \in [1, 2^{2018}]$, find the "average value" of the function $f(x)$ on $[1, 2^{2018}]$.

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