
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
Let the function $f(x)=1+(1+a)x-x^{2}-x^{3}$, where $a > 0$.  
(I) Discuss the monotonicity of $f(x)$ over its domain;  
(II) When $x \in [0,1]$, find the values of $x$ for which $f(x)$ attains its maximum and minimum values.

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