
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 $y$: 

\[
\left\{
\begin{array}{l}
2x+y=4m \\
x+2y=2m+1
\end{array}
\right.
\]

where $m$ is a constant real number. 

(1) If $x+y=1$, find the value of the real number $m$.

(2) If $-1\leqslant x-y\leqslant 5$, find the range of values for $m$.

(3) Under the conditions of (2), simplify: $|m+2|+|2m-3|$.

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