
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 $f(x) = e^x(x+1) - (x^2 + 4x)$,

$(1)$ Find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,1)$;

$(2)$ Discuss the monotonicity of $f(x)$ and find the maximum value of $f(x)$.

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