
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 quadratic function $f(x)=-x^{2}+bx+c$ with respect to $x$, it is always true for any real number $x$ that $f(2+x)=f(2-x)$.

1. Find the value of the real number $b$.
2. When $a∈R$, compare the sizes of $f(\frac{5}{4})$ and $f(-a^{2}-a+1)$, and explain the rationale.

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