
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 $f(x)=|mx+3|-|2x+n|$.
- $(1)$ When $m=2$, $n=-1$, find the solution set of the inequality $f(x) < 2$.
- $(2)$ When $m=1$, $n < 0$, the area of the triangle formed by the graph of $f(x)$ and the $x$-axis is greater than $24$, find the range of values for $n$.

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