
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 the function $f(x)$ has a period of 4, and when $x \in (0, 4]$, $f(x)$ is defined as $$f(x) = \begin{cases} \cos{\frac{\pi x}{2}}, & 0 < x \leq 2 \\ \log_{2}{(x - \frac{3}{2})}, & 2 < x \leq 4 \end{cases}$$, find the value of $f(f(-\frac{1}{2}))$.

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