
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
Read the following material:<br/>We define: If the solution to the one-variable linear equation $ax=b$ involving $x$ is $x=b+a$, then we call this equation a "sum solution equation." For example, the solution to the equation $2x=-4$ is $x=-2$, and since $-2=-4+2$, the equation $2x=-4$ is a "sum solution equation." Please answer the following questions based on the above rules:<br/>$(1)$ The following one-variable linear equations involving $x$ are "sum solution equations":<br/>①$\frac{2}{3}x=-\frac{2}{3}$<br/>②$-3x=\frac{9}{4}$<br/>③$5x=-2$<br/>$(2)$ If the one-variable linear equation involving $x$ is $3x=2a-10$ and is a "sum solution equation," find the value of $a$.

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