
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 $f(x)=x^{3}$.

    $(1)$ Find the equation of the tangent line to the graph of $f(x)$ at the point $(1,1)$;

    $(2)$ If the graph of $f(x)$ is curve $C$, and a tangent line is drawn from point $P\left( \frac{2}{3},0\right)$ to curve $C$, find the equation of the tangent line.

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