
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
Let $a$ be the extreme value point of the function $g(x) = \frac{4}{3}x^3 + 2x^2 - 3x - 1$, and the function $f(x)$ is defined as follows:

$$
f(x) =
\begin{cases}
a^x, & \text{if } x < 0 \\
\log_a{x}, & \text{if } x \geq 0
\end{cases}
$$

Find the value of $f(\frac{1}{4}) + f(\log_2{\frac{1}{6}})$ equal to $\_\_\_\_\_\_$.

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