
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 that the function $f(x) = e^x + \frac{x^2}{2} + \ln(x + m) + n$ has a tangent line at the point $(0, f(0))$ with the equation $(e + 1)x - ey + 3e = 0$.

(1) Find the explicit formula for $f(x)$.
(2) If $f(x) \geq \frac{x^2}{2} + ax + 3$ holds for $x \geq 0$, find the range of the real number $a$.

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