
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 that the function $f(x)$ is defined on the domain $\mathbb{R}$, it is an odd function and also a periodic function with a period of $3$. When $x \in (0, \frac{3}{2})$, $f(x) = \sin \pi x$, and $f(\frac{3}{2}) = 0$. Determine the number of zeros of the function $f(x)$ on the interval $[0, 6]$.

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