
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
Read the following material: Answer the question "Given $x-y=2$, and $x \gt 1$, $y \lt 0$, determine the range of $x+y" with the following solution: Solution: Since $x-y=2$, therefore $x=y+2$. Also, since $x \gt 1$, therefore $y+2 \gt 1$. Therefore, $y \gt -1$. Also, since $y \lt 0$, therefore $-1 \lt y \lt 0. \ldots $① Similarly, we get: $1 \lt x \lt 2. \ldots $② From ① + ②, we get $-1+1 \lt y+x \lt 0+2$. Therefore, the range of $x+y$ is $0 \lt x+y \lt 2$. Please complete the following questions using the above method: (1) Given $x-y=4$, and $x \gt 3$, $y \lt 1$, then the range of $x+y$ is ______. (2) Given $y \gt 1$, $x \lt -1$, if $x-y=m$ holds, find the range of $x+y$ (express the result in terms of $m$).

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