
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 odd function $f(x)$ defined on $\mathbb{R}$ satisfies $f(x+\pi)=f(-x)$, and $f(x)=\sqrt{x}$ when $x\in[0,\frac{\pi}{2}]$, find the sum of all the zeros of the function $g(x)=(x-\pi)f(x)-1$ in the interval $[-{\frac {3\pi }{2}},3\pi ]$.

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