
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
Let the function $f(x)=ae^x(x+1)$ (where $e=2.71828…$), and $g(x)=x^2+bx+2$. It is known that they have the same tangent line at $x=0$.

(1) Find the expressions for functions $f(x)$ and $g(x)$;

(2) Find the minimum value of the function $f(x)$ on the interval $[t, t+1]$ ($t > -3$);

(3) If for all $x \geqslant -2$, $kf(x) \geqslant g(x)$ always holds, find the range of values for the real number $k$.

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