
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 $f(x) = ax^{2} + \ln x - x$, where $a \in \mathbb{R}$ and $a \neq 0$.
(1) When $a = -1$, determine the intervals of monotonicity and the extreme values of the function $f(x)$;
(2) If $f(x) < 2ax$ holds true for all $x > 1$, determine the range of values for $a$.

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