
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 function $f(x)$ defined on $\mathbb{R}$ with a period of $3$, and $$f(x) = \begin{cases} 4x^2 - 2 & \text{if } -2 \leq x \leq 0, \\ x & \text{if } 0 < x < 1, \end{cases}$$ find $f(f(\frac{21}{4}))$.

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