
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 $f(x) = \begin{cases} \log_2(1-x^2) & \text{if } -1 < x < 1 \\ \sin(\frac{\pi x}{3}) & \text{if } x \geq 1 \end{cases}$, find the value of $f(\frac{31}{2}) + f(\frac{\sqrt{3}}{2})$.

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