
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 $f(x) = ae^x(x+2)$, $g(x) = x^2 + bx + 2$, given 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 $[t, t+1]$ ($t > -4$).

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