
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
Suppose that $f(x)$ and $g(x)$ are functions on $\mathbb{R}$ such that the range of $f$ is $[-7,4]$ and the range of $g$ is $[-3,2]$. Find the maximum value of a number $b$ such that $b$ is in the range of $f(x) \cdot g(x)$.

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