
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 $y$: $\left\{\begin{array}{l}{3x+2y=8+a}\\{2x+3y=3a}\end{array}\right.$, the following conclusions are drawn:<br/>① When $x$ and $y$ are opposite numbers, $a=-2$;<br/>② Regardless of the value of $a$, the solution to this system of equations is also a solution to the equation $x-y=8-2a$;<br/>③ Regardless of the value of $a$, the value of $7x+3y$ remains constant;<br/>④ $x=-\frac{3}{7}y+\frac{24}{7}$. The correct conclusions are ______ (fill in the numbers).

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