
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) = log₂x and g(x) = 2x + a, if there exist $x_1, x_2 \in [\frac{1}{2}, 2]$ such that f($x_1$) = g($x_2$), find the range of values for a.

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