
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 graph of the function $f(x) = e^{x} + ax + b$ has a tangent line at the point $(0, f(0))$ with the equation $2x - y + 1 = 0$.  
$(1)$ Find the expression for $f(x)$.  
$(2)$ For $x > 0$, if $f(x) \geq x^{2} + mx + 1$ always holds, find the range of real numbers for $m$.

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