
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
(1) The maximum value of the function $f(x)=-x^{2}+2x+3$ in the interval $[2,3]$ is _______.

(2) The graph of the function $y=3^{x-4}+b$ always passes through the fixed point $(4,6)$. Then $b=$ _______.

(3) Given that the function $f(x)=\begin{cases}4x-6, & x < 2 \\ x^{2}-2ax, & x\geqslant 2\end{cases}$ is an increasing function on $\mathbb{R}$, the range of the real number $a$ is _______.

(4) Given that $f(x)$ is an odd function on $\mathbb{R}$ and satisfies $f(x+4)=f(x)$, when $x \in (0,2)$, $f(x)=2x^{2}$. Then $f(7)=$ _______.

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