
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 functions $f(x)=ae^{x}(x+2)$ 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 the functions $f(x)$ and $g(x)$;

(2) Find the minimum value of the function $f(x)$ on the interval $[t,t+1]$ where $t > -4$.

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