
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 \( y = f(x) \) be a function defined on the set of real numbers. Consider the following four propositions:

(1) If \( f(2x) = 2f(x) \), then the graph of \( y = f(x) \) is a straight line.

(2) If \( f\left(\frac{1}{x}\right) = \frac{1}{f(x)} \) (for \( x \neq 0 \)), then the graph of \( y = f(x) \) is a hyperbola.

(3) If \( f(x + 2) = f(x - 2) \), then the graph of \( y = f(x) \) is periodic.

(4) If \( f(4 - x) = f(x) \), then the graph of \( y = f(x) \) is symmetric.

Among these, the proposition(s) that are true is(are): ________.

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