
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 a function $f(x)$ defined on $\mathbb{R}$ that is both odd and periodic with a period of $3$, and for $x \in \left(0, \frac{3}{2}\right)$, $f(x) = \sin(\pi x)$, $f\left(\frac{3}{2}\right) = 0$, determine the number of zeros of the function $f(x)$ in the interval $[0,6]$.

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