
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 $f(x) = \log_a(x+1)$ where $a > 0$ and $a \neq 1$,

(1) Find the solution set for the inequality $f(x) > 0$;

(2) If $a > 1$ and the range of $f(x)$ on the interval $[m, n]$ ($-1 < m < 0$) is $[\log_a \frac{p}{m}, \log_a \frac{p}{n}]$, find the range of the real number $p$.

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