
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 functions $f(x)=2|\ln(x)|$ and $g(x)=\begin{cases} 0, & 0 < x\leqslant 1 \\ |x^{2}-4|-2, & x > 1 \end{cases}$, determine the number of real roots of the equation $|g(x)-f(x)|=1$.

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