
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
$(1)$ If $12 \lt a \lt 60$ and $15 \lt b \lt 36$, find the range of values for $2a-b$ and $\frac{a}{b}$;<br/>$(2)$ Given that $x$ and $y$ satisfy $-\frac{1}{2}＜x-y＜\frac{1}{2}$ and $0 \lt x+y \lt 1$, find the range of values for $3x-y$.

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