
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 $f(x)$ is a quadratic function, $f(0) = 2$, and it satisfies $f(x + 1) - f(x) = 2x - 1$.
1. Find the expression for $f(x)$;
2. When $x \in [-2, 2]$, find the range of the function;
3. When $x \in [t, t + 1]$, find the minimum value of $f(x)$.

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