
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 $f(x)=x^{3}+3px^{2}+3px+1$.

(1) Can this function take an extreme value at $x=-1$? If so, find the value of the real number $p$; if not, explain the reason.

(2) If this function is an increasing function on the interval $(-1,+\infty)$, find the range of values for the real number $p$.

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