
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
If the quadratic function $f(x)=ax^{2}+bx+c(a,b,c∈R)$ satisfies $f(x+1)-f(x)=4x+1$, and $f(0)=3$.
1. Find the analytical expression of $f(x)$;
2. Let $g(x)=f(2^{x})$, find the maximum and minimum values of $g(x)$ on $[-3,0]$.

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