
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 $f(x)=|2x-1|-|x-a|$, where $a\leqslant 0$.
$(1)$ When $a=0$, find the solution set for the inequality $f(x) < 1$;
$(2)$ If the area of the triangle formed by the graph of $f(x)$ and the x-axis is greater than $\dfrac{3}{2}$, find the range of values for $a$.

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