
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
Given the three functions $y=2^{x}$, $y=\log _{2}x$, and $y=x^{\frac {1}{2}}$, find the number of functions that satisfy the condition $f(\frac{x_{1}+x_{2}}{2}) < \frac{f(x_{1})+f(x_{2})}{2}$ for all $0 < x_{1} < x_{2} < 1$.

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