
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 that the quadratic function $f(x) = x^2 + ax + b$ is symmetrical about $x=1$ and its graph passes through the origin:
1. Find the explicit expression for this function.
2. Determine the range of the function when $x \in (0, 3]$.

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