
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
$(1)$ Given real numbers $x$ and $y$ satisfying $-1\leqslant x\leqslant 2$ and $0\leqslant y\leqslant 1$, find the range of $x-2y$;<br/>$(2)$ Given $-1 \lt a+b \lt 3$ and $2 \lt a-b \lt 4$, find the range of $2a+3b$.

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