
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 an odd function $f(x)$ defined on $\mathbb{R}$ is symmetric about the line $x=1$, and when $0 < x \leq 1$, $f(x) = \log_{3}x$, find the sum of all real roots of the equation $f(x) + 4 = f(0)$ in the interval $(0, 10)$.

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