
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 $2$. For $x \in [-1, 1)$, $f(x)$ is given by
$$
f(x) = 
\begin{cases} 
-4x^{2}+1, & -1 \leq x < 0 \\ 
x + \frac{7}{4}, & 0 \leq x < 1 
\end{cases}
$$
Find the value of $f\left(f(\frac{3}{2})\right)$.

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