
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 equation \(2y = \log_{a} x \ (x > 1, \ a > 1)\), there are points \(A\), \(B\), and \(C\) on its graph with x-coordinates \(m\), \(m+2\), and \(m+4\). If the area of \(\triangle ABC\) is \(S = f(m)\), determine the range of \(f(m)\).

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