
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
The function $f(x)$ satisfies $f(x+4)=f(x)$ $(x \in \mathbb{R})$, and in the interval $(-2,2]$, $f(x)= \begin{cases} \cos \frac {\pi x}{2}, & 0 < x\leqslant 2 \\ |x+ \frac {1}{2}|, & -2 < x\leqslant 0 \end{cases}$. Find the value of $f(f(15))$.

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