
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 $f(x)=a\ln x-x^{2}$, where $a\in\mathbb{R}$.
(1) Discuss the monotonicity of $f(x)$;
(2) For any two distinct real numbers $p$, $q$ in $(0,1)$, it is always true that $\frac{f(p+1)-f(q+1)}{p-q}>1$. Find the range of values for $a$.

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