
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 $f(x)=e^{x}-\sin x-\cos x-\frac{1}{2}ax^{2}$ where $a\in \mathbb{R}$, and ${f'}(x)$ is the derivative of the function $f(x)$.
$(1)$ If the tangent line of the curve $y=f(x)$ at the point $(\frac{\pi}{4},f(\frac{\pi}{4}))$ is parallel to the line $y=(e^{\frac{\pi}{4}}-\pi)x+1$, find the value of the real number $a$;
$(2)$ If the inequality ${f'}(x)\geqslant \ln(1-x)$ holds for all $x\in (-\infty, 1)$, find the value of the real number $a$.

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