
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 function \( f(x) \) is an even function and has a period of 4, if the equation \( f(x) = 0 \) has exactly one root, which is 1, in the interval \([0,2]\), what is the sum of all the roots of \( f(x) = 0 \) in the interval \([0,17]\)?

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