
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
Define the function $y=f(x)$, where $x \in I$. If there exists a constant $M$ such that for any $x_1 \in I$, there exists a unique $x_2 \in I$ making $$\frac {f(x_{1})+f(x_{2})}{2}=M$$, then the function $f(x)$ is said to have an "average" of $M$ on $I$. Given $f(x)=x^2+\log_{2}x$, $x \in [1,4]$, find the "average" of the function $f(x)=x^2+\log_{2}x$, $x \in [1,4]$.

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