
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 $f\left(x\right)=\left(x-1\right)\left(x-a\right)^{2}$ attains a local minimum at $x=0$.  
$(1)$ Find the value of $a$;  
$(2)$ If the tangent line $l$ at point $P$ on the curve $y=f\left(x\right)$ is parallel to the tangent line at $x=1$, find the equation of $l$.

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