
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) Solve the inequality with respect to $x$: $mx+4 \lt m^{2}+2x$, where $m \gt 2$;<br/>(2) Let $x \gt y \gt 0$, compare the sizes of $\frac{x}{{1+x}}$ and $\frac{y}{{1+y}}$.

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