
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
If the odd function \( y=f(x) \) defined on \( \mathbf{R} \) is symmetrical about the line \( x=1 \), and when \( 0 < x \leqslant 1 \), \( f(x)=\log_{3}x \), find the sum of all real roots of the equation \( f(x)=-\frac{1}{3}+f(0) \) in the interval \( (0,10) \).

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