
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 $f(x) = ax^2 + bx$ (where $a$ and $b$ are constants, and $a \neq 0$) that satisfies the conditions: $f(2) = 0$, and the equation $f(x) = x$ has two equal real roots.
(1) Find the expression for $f(x)$ and state the range of the function;
(2) Compare the values of $f(0)$, $f(1)$, and $f(3)$;
(3) If $x_1 < x_2 < 1$, compare the values of $f(x_1)$ and $f(x_2)$.

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