
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 $f(x)= \begin{cases} \sin \pi x & \text{if } x\geqslant 0\\ \cos \left( \frac {\pi x}{2}+ \frac {\pi}{3}\right) & \text{if } x < 0\end{cases}$. Evaluate $f(f( \frac {15}{2})$.

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