
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 $f(x) = (x - 1)e^x - a(x^2 + 1)$, where $x \in [1, +\infty)$.
(1) Discuss the monotonicity of $f(x)$;
(2) If $f(x) \geq -2a + \ln x$, find the range of values for the real number $a$.

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