
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 the function $f(x)$, it is known that for any $x \in [0, +\infty)$, the equation $f(x+2) = f(x)$ holds, and when $x \in [0, 2)$, $f(x) = 2 - x$. The sum of all roots of the equation $f(x) = \frac{1}{n}x$ in the interval $[0, 2n)$ (where $n \in \mathbb{N}^*$) is \_\_\_\_\_\_.

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