
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
1. Given non-negative real numbers \( x, y, z \) satisfy \( x^{2}+y^{2}+z^{2}+x+2 y+3 z=\frac{13}{4} \). Then \( (x+y+z)_{\text {max }}= \) 

2. Given \( f(x) \) is an odd function defined on \(\mathbb{R}\) and has a period of 3. When \( x \in \left(0, \frac{3}{2}\right) \), \( f(x)=\ln \left(x^{2}-x+1\right) \). The number of zeros of the function \( f(x) \) in the interval \([0,6]\) is 

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