
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 \\(a > 1\\), the function \\(f(x)=\log_{a}x\\) has the difference between its maximum and minimum values on the interval \\([a,2a]\\) equal to \\(\frac{1}{2}\\). Let's find the value of \\(a\\.

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