
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 $y$: $\left\{\begin{array}{l}x-2y=3-a\\ x+y=2a\end{array}\right.$, where $-2\leqslant a\leqslant 0$. The following conclusions are made: ① When $a=0$, the values of $x$ and $y$ are opposite numbers; ② $\left\{\begin{array}{l}x=2\\ y=0\end{array}\right.$ is a solution to the system of equations; ③ When $a=-1$, the solution to the system of equations is also a solution to the equation $2x-y=1-a$. The correct conclusions are ____.

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