
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 function $f(x) = ax^2+bx+c$ ($a \neq 0$ and $a, b, c$ are constants), it satisfies $f(0)=1$, $f(1)=6$, and for all $x \in R$, $f(-2+x) = f(-2-x)$ always holds.
(1) Find the analytical expression for $f(x)$.
(2) If $f(x)$ is not monotonic on the interval $[a-1, 2a+1]$, find the range of real numbers for $a$.

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