
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 $f\left(x\right)=x^{4}+x^{2}+\left(a-1\right)x+1$.  
$(1)$ When $a=1$, discuss the monotonicity of $f\left(x\right)$;  
$(2)$ Given $x \gt 0$, $e^{x} \gt x+1$ always holds true. If $f\left(x\right)\leqslant x^{4}+e^{x}$ always holds true for $x \gt 0$, find the range of values for $a$.

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