
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
For any two real numbers $a$ and $b$, define $\min(a, b) = \begin{cases} a, & a < b \\ b, & a \geqslant b \end{cases}$. If $f(x) = 4 - x^2$ and $g(x) = 3x$, find the maximum value of $\min(f(x), g(x))$.

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