
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 that $f(x)$ is a periodic function defined on $\mathbb{R}$ with a period of $2$, when $x \in (-1, 1]$, $f(x)=\begin{cases} -4x^{2}+ \frac{9}{8},-1 < x\leqslant 0, \\ \log _{2}x,0 < x\leqslant 1, \end{cases}$, find the value of $f(f( \frac{7}{2}))=\_\_\_\_\_\_\_\_$.

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