
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 $-1 \lt x \lt 4$, $2 \lt y \lt 3$, find the range of $x-y$;<br/>$(2)$ Compare the values of $\left(x-1\right)(x^{2}+x+1)$ and $\left(x+1\right)(x^{2}-x+1)$, where $x\in R$.

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