
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 $f(x)=2{{e}^{x}}-2ax-{{a}^{2}}+3$, where $a\in R;$ and $e$ is the base of the natural logarithm.

(1) Discuss the monotonicity of the function $f(x)$;

(2) If the inequality $f(x)-{{x}^{2}} \geqslant 0$ holds for any $x \geqslant 0$, find the range of values of the real number $a$.

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