
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
If a function \( y = f(x) \) satisfies that for every value \( x_1 \) in its domain, there exists a unique \( x_2 \) in the domain such that \( f(x_1) f(x_2) = 1 \), then the function is called a "dependent function." Identify which of the following propositions are true:
1. \( y = \frac{1}{x^2} \) is a dependent function.
2. \( y = \sqrt{2} + \sin x \) \( (x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]) \) is a dependent function.
3. \( y = 2^x \) is a dependent function.
4. \( y = \ln x \) is a dependent function.
5. If \( y = f(x) \) and \( y = g(x) \) are both dependent functions, and their domains are the same, then \( y = f(x) g(x) \) is a dependent function.

Identify the sequence numbers of the true propositions.

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