
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 $y=f(x)=\begin{cases} & |\lg x|, x > 0 \\ & 2x+6, x\leqslant 0 \\ \end{cases}$, if $a$, $b$, $c$ are distinct, and $f(a)=f(b)=f(c)$, determine the range of values for $abc$.

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