
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 the even function $f\left( x \right)=\begin{cases} \left| \log_{4}x \right|, & 0 < x\leqslant 4 \\ f\left( 8-x \right), & 4 < x < 8 \\ \end{cases}$ and $f\left( x-8 \right)=f\left( x \right)$, determine the number of zeros of the function $F\left( x \right)=f\left( x \right)-\dfrac{1}{{{2}^{\left| x \right|}}}$ in the interval $\left[ -2018,2018 \right]$.

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