
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
In the Cartesian coordinate system, if two points A(a, b) and B(-a, -b) are on the graph of the function $y=f(x)$, then $[A, B]$ is called a pair of points symmetric about the origin for the function $f(x)$. Determine the number of pairs of points symmetric about the origin for the function $$g(x)= \begin{cases} \cos \frac {\pi}{2}x, & x\leq0 \\ \log_{4}(x+1), & x>0\end{cases}$$

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