
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
If the quadratic function $f(x) = -x^2 + bx + c$ satisfies $f(2 + x) = f(2 - x)$ for all real numbers $x$,  
(1) Find the value of the real number $b$;  
(2) When $a \in \mathbb{R}$, compare $f\left(\frac{5}{4}\right)$ with $f(-a^2 - a + 1)$ and explain the reasoning.

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