
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 functions $f(x)=-2x^{3}+6ax^{2}-1$ and $g(x)=e^{x}-2ax-1$, where $a\in R$.<br/>$(1)$ Discuss the monotonicity of the function $f(x)$;<br/>$(2)$ If $a \gt 0$, $\exists x_{1}\in \left(0,+\infty \right)$, $\exists x_{2}\in R$ such that $f(x_{1})\geqslant g(x_{2})$ holds, find the range of real number $a$.

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