
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 3. When $x \in [-2, 1)$, $f(x)$ is defined as follows:
$$
f(x) = \begin{cases}
4x^2-2 & -2 \leq x \leq 0 \\
x & 0 < x < 1
\end{cases}
$$
Calculate $f(f(\frac{21}{4}))$.

A) $-\frac{1}{4}$  
B) $\frac{3}{4}$  
C) $\frac{1}{4}$  
D) 0

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