
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 function $f(x)=\begin{cases}|\ln x|, & x > 0 \\ 2x+3, & x\leqslant 0\end{cases}$

   (1) Find the intervals of monotonicity for the function $y=f(x)$;

   (2) If the line $y=m$ intersects the graph at three points, from left to right, denoted as $A(x_{1},y_{1})$, $B(x_{2},y_{2})$, and $C(x_{3},y_{3})$, find the range of values for $s=x_{1}+x_{2}\cdot x_{3}$.

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