
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: for two distinct real numbers $a$ and $b$, we define $\max \{a,b\}$ as the larger value between $a$ and $b$. For example, $\max \{2,4\}=4$, and $\max \{-2,-4\}=-2$. According to this definition, if $\max\{x,-x\}=\frac{x^{2}-3x-2}{2}$, then the value of $x$ is ____.

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