
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 $f(x)=kx^{2}-kx$ and $g(x)= \begin{cases} \ln x,x\geqslant 1 \\ -x^{3}+(a+1)x^{2}-ax,0 < x < 1\\end{cases}$, find the unique value of real number $a$ such that the inequality $f(x)\geqslant g(x)$ holds for all positive real numbers $x$.

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