
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 \( (0, +\infty) \), and the range is \( (-1, 4) \). For any unequal positive real numbers \( x_{1} \) and \( x_{2} \) within the domain, it holds that \( f(x_{1}) + f(x_{2}) < 2 f\left(\frac{x_{1} + x_{2}}{2}\right) \). Please provide two different types of functions that satisfy this condition.

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