
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 $f(x)$ be a function defined on $\mathbb{R}$ with a period of $2$. When $x \in [-1,1)$, 
$$
f(x)=\begin{cases} 
-4x^{2}+2, & -1\leqslant x < 0 \\
2x, & 0\leqslant x < 1 \\
\end{cases}
$$
then $f[f(\frac{4}{3})]=$ __________.

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