
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]


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Given a cubic function $f(x)=\frac{a}{3}x^{3}+bx^{2}+cx+d$ ($a < b$) is monotonically increasing on $\mathbb{R}$, then the minimum value of $\frac{a+2b+3c}{b-a}$ is ______.

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