
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
Let \\(f(x)\\) be defined on \\((-∞,+∞)\\) and satisfy \\(f(2-x)=f(2+x)\\) and \\(f(7-x)=f(7+x)\\). If in the closed interval \\([0,7]\\), only \\(f(1)=f(3)=0\\), then the number of roots of the equation \\(f(x)=0\\) in the closed interval \\([-2005,2005]\\) is      .

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