
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 \( f(x)=\log _{a} \frac{x-2a}{x+2a} \) where \( a > 0 \) and \( a \neq 1 \), if \( x \) is in the interval \([s, t]\), and \( f(x) \) is in the interval \(\left[\log _{a}(t-a), \log _{u}(s-a)\right]\), find the range of the real number \( a \).

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