
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
Set \( A \) consists of functions \( f(x) \) that satisfy the following property: for any \( x > 0, y > 0 \) with \( x \neq y \), it holds that \( f(x) + 2 f(y) > 3 f\left(\frac{x + 2 y}{3}\right) \). Determine whether the following functions are in set \( A \) (answer yes or no):
(1) \( f_{1}(x) = \log_{2} x \)
(2) \( f_{2}(x) = (x + 2)^{2} \)

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