
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
The domain of the function \( y = f(x) \) is \( D \). If, for any \( x_1 \in D \), there exists a unique \( x_2 \in D \) such that \( f(x_1) + f(x_2) = 2008 \) holds, then \( x_2 \) is called the "Olympic number" of \( x_1 \). Given the following five functions:
1. \( y = 2008 x^2 \)
2. \( y = 2008 x^3 \)
3. \( y = 2008 \cos x \)
4. \( y = \lg(2008x) \)
5. \( y = 2008^x \)

Identify which of these functions have the "Olympic number" property. Fill in the numbers of the functions you think meet the requirement.

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