
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 that the domain of function f(x) is D, if for any x\_1 in D, there exists x\_2 in D such that $\frac{f(x_{1}) + f(x_{2})}{2} = m$ (where m is a constant), then the function f(x) is said to have an arithmetic mean of m on D. Write out the arithmetic mean m of the function f(x) = log\_2⁡x on the interval [4, 16].

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