
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
Define a new operation: $\left(a,b\right)\cdot \left(c,d\right)=ac+bd$, where $a$, $b$, $c$, $d$ are real numbers. For example, $\left(1,2\right)\cdot \left(3,4\right)=1\times 3+2\times 4=11$. If $\left(2x,3\right)\cdot \left(3,-1\right)=3$, then $x=\_\_\_\_\_\_$.

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