
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 a function \( f(x) \) defined on \( \mathbf{R} \) such that for any real number \( x \), \( f(2+x) = f(2-x) \) and \( f(7+x) = f(7-x) \), and on the interval \([0,7]\), only \( f(1) = f(3) = 0 \).

(1) Determine the parity (odd or even nature) of \( f(x) \).

(2) Find the number of solutions to the equation \( f(x) = 0 \) in the interval \([-2005, 2005]\).

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