
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 $g(x)=x^{2}-2ax$, $f\left( x \right)=\dfrac{1}{3}{{x}^{3}}-\ln \left( x+1 \right)$, if for any $x_{1} \in [0,1]$, there exists $x_{2} \in [1,2]$ such that $f''\left( x_{1} \right) \geqslant g\left( x_{2} \right)$ holds, then the range of the real number $a$ is _______.

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