
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 $f(x)=2{{e}^{x}}-{{(x-a)}^{2}}+3$, where $a\in R$.

(1) Find the value of $a$ if the tangent line of the function $y=f(x)$ at $x=0$ is parallel to the $x$-axis.

(2) Find the range of $a$ if $f(x)\geqslant 0$ always holds when $x\geqslant 0$.

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