
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
Proposition $p$: The function $f(x)=x^{3}+ax^{2}+ax$ is monotonically increasing on $R$. Proposition $q$: The equation $\frac{x^{2}}{a+2}+ \frac{y^{2}}{a-2}=1$ represents a hyperbola.
(1) Determine the truth of proposition $p$ when $a=1$ and explain the reason.
(2) If the proposition "$p$ and $q$" is true, find the range of values for the real number $a$.

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