
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 $f(x) = \lg \frac{x+5}{x-5}$.
① Find the domain of $f(x)$;
② Determine the parity of $f(x)$;
③ Find $f^{-1}(x)$;
④ Find the range of $x$ for which $f(x) > 0$.

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