
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 function \( f(x) = \left|\log_{2} x\right| \), if the real numbers \( a \) and \( b \) (where \( a < b \)) satisfy \( f(a) = f(b) \), then find the range of values for \( a + 2014b \).

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