
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
Determine the number of zeros for the function $f(x)$, which is defined on $\mathbb{R}$ as an odd function with a period of 3, and given that $f(x) = \sin(\pi x)$ when $x \in (0, \frac{3}{2})$. Find the number of zeros that $f(x)$ has within the interval $[0, 5]$.

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