
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 $y$: $\left\{\begin{array}{l}2x+y=4-m\\ x-2y=3m\end{array}\right.$.① When $m=1$, the solution to the system of equations is $\left\{\begin{array}{l}x=\frac{9}{5}\\ y=-\frac{3}{5}\end{array}\right.$; ② Regardless of the value of $m$, the solution to the system of equations is the solution to the linear equation in $x$ and $y$: $3x-y=4+2m$; ③ The solutions $x$ and $y$ of the system of equations can both be negative numbers. The correct statements are ______. (Fill in the corresponding numbers)

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