
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 functions f(x) = log<sub>2</sub>x and g(x) = sqrt(x) + sqrt(a - x) (a > 0), if for all x<sub>1</sub> in the domain of g(x), there exists an x<sub>2</sub> in the interval [4, 16] such that g(x<sub>1</sub>) = f(x<sub>2</sub>), then the range of values for the real number a is _______.

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