
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
Given the logarithmic function $f(x) = \log_a x$ where $a > 0$ and $a \neq 1$, the product of its maximum and minimum values in the interval $[2, 4]$ is $2$. Find the value of $a$.
A) $\frac{1}{2}$
B) $\frac{1}{2}$ or $2$
C) $2\sqrt{2}$
D) $2$

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