
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
We define: For any real numbers $a$, $b$, $c$, $d$, $\left[a,b\right]*\left[c,d\right]=ac-bd$, where the right side of the equation represents the usual multiplication and subtraction operations (e.g., $\left[3,2\right]*\left[5,1\right]=3\times 5-2\times 1=13)$. If $\left[-x,3\right]*\left[x-2,-6\right]=10$, then the value of $x$ is ______.

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