
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 a quadratic function $f(x)$ such that $f(0)=1$, and $f(x+1)-f(x)=2x$.
(I) Find the explicit expression for $f(x)$.
(II) Find the maximum and minimum values of $f(2^x)$ on the interval \[-1, 1\].

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