
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 function f(x) = ax^2 + bx + c (a ≠ 0), it satisfies f(0) = 2 and f(x + 1) - f(x) = 2x - 1.

1. Find the analytic expression of function f(x);
2. Find the monotonic intervals of function f(x);
3. Find the maximum and minimum values of the function when x ∈ [-1, 2].

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