
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 a function $f(x)=({ax-\frac{3}{4}}){e^x}-\frac{{b{e^x}}}{{{e^x}+1}}$, where $a$, $b\in \mathbb{R}$, and $e$ is the base of the natural logarithm.<br/>$(1)$ When $b=0$, discuss the monotonicity of the function $f(x)$;<br/>$(2)$ When $b=1$, if $f(x)≥-\frac{5}{4}$ holds for all $x\in \left[-2,+\infty \right)$, find the value of $a$.

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