
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 $f(x)=e^{x}- \dfrac {x^{2}}{2}-ax-1$ (where $a\in\mathbb{R}$ and $e$ is the base of the natural logarithm):  
(1) Let $g(x)=f(x)+ \dfrac {x^{2}}{2}$, discuss the monotonicity of the function $g(x)$.  
(2) When $x \geqslant 1$, the inequality $f(x)\geqslant 0$ is always satisfied; find the range of the real number $a$.

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