
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
Arrange four numbers $a$, $b$, $c$, $d$ into $|\begin{array}{l}{a}&{c}\\{b}&{d}\end{array}|$, which we call a second-order determinant. We define its operation as: $|\begin{array}{l}{a}&{c}\\{b}&{d}\end{array}|=ad-bc$. If $|\begin{array}{l}{x+3}&{x-3}\\{x-3}&{x+3}\end{array}|=12$, then $x=\_\_\_\_\_\_$.

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