
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 $f(x)=x^{3}+ax^{2}+x+1$, where $a\in\mathbb{R}$.

$(1)$ Find the intervals of monotonicity for the function $f(x)$.

$(2)$ If the function $f(x)$ is decreasing on the interval $\left( -\frac{2}{3},-\frac{1}{3} \right)$, find the range of values for $a$.

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