
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 $f(x)=|\ln x|$ and $g(x)=\begin{cases}0, & 0 < x\leqslant 1 \\ |\ x^2-4|-2, & x > 1\end{cases}$, find the range of values of $a$ for which the equation $|f(x)+g(x)|=a$ has $4$ real roots.

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