
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 $f\left(x\right)=x^{3}-ax^{2}-a^{2}x$.  
$(1)$ If one of the extreme points of $f\left(x\right)$ is $1$, find the minimum value of $f\left(x\right)$.  
$(2)$ If $a=1$, find the equation of the line passing through the origin and tangent to the curve $y=f\left(x\right)$.

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