
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
Define the function $f(x)=x^{2}+x$ on the set of real numbers $R$, and $g(x)=\frac{1}{3}x^{3}-2x+m$.

$(1)$ Find the equation of the tangent line to the graph of $f(x)$ at $x=1$.

$(2)$ If $f(x) \geqslant g(x)$ holds for any $x \in [-4,4]$, find the range of the real number $m$.

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