
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
Given the system of equations in terms of $x$ and $y$: $\left\{\begin{array}{l}x+y=m+2\\4x+5y=6m+3\end{array}\right.$ has a solution of a pair of positive numbers.<br/>$(1)$ Find the range of values for $m$;<br/>$(2)$ Simplify $|2m-5|-|m-7|$.

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