
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 function $f(x)$ be a periodic function with a period of $2$ defined on $\mathbb{R}$. When $x \in [-1, 1)$, $f(x) = \begin{cases} -4x^2 + 1, & -1 \leq x < 0 \\ x + \frac{7}{4}, & 0 \leq x < 1 \end{cases}$. Find $f[f(\frac{3}{2})]$.

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