
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 $f(x) = (ax + b)e^x$, where $e$ is the base of the natural logarithm, and $b$ is the real part of the complex number $\frac{3i-2}{i}$.
(1) Find the intervals where the function $f(x)$ is monotonic.
(2) Let the function $g(x) = \frac{1}{2}x - \ln(x) + t$. When $a = -1$, there exists $x \in (0, +\infty)$ such that $f(x) \leq g(x)$ holds. Find the range of $t$.

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