
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
If the function $f(x)= \frac{1}{3}x^{3}- \frac{1}{2}ax^{2}+(a-1)x+1$ is decreasing on the interval $(1,4)$ and increasing on the interval $(6,+\infty)$, then the range of the real number $a$ is __________.

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