
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 $f(x)=\frac{1}{3}x^{3}+x^{2}+ax$.

(1) Discuss the monotonicity of $f(x)$;

(2) Suppose $f(x)$ has two extreme points $x_{1}$, $x_{2}$, and the line $l$ passing through the two points $(x_{1},f(x_{1}))$, $(x_{2},f(x_{2}))$ intersects the $x$-axis at a point on the curve $y=f(x)$, find the value of $a$.

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