
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 $f(x) = -2x^2 + ax + b$ and $f(2) = -3$.

(1) If the graph of the function $f(x)$ is symmetric about the line $x=1$, find the range of $f(x)$ in the interval $[-2, 3]$.

(2) If the function $f(x)$ is decreasing in the interval $[1, +\infty)$, find the range of the real number $b$.

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