
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) Observe the following expressions: $7^{2}=49$, $7^{3}=343$, $7^{4}=2401$, ..., then the last two digits of $7^{2017}$ are ______.

(2) Given the function $f(x)=x^{3}+ax^{2}+bx$ has an extremum of $10$ at $x=1$, then $f(2)$ equals ______.

(3) If $f(x)=x^{2}-2x-4\ln x$, then the solution set of $f'(x) > 0$ is ______.

(4) Given the function $f(x)=e^{x}(x-b)$ $(b \in R)$. If there exists $x \in \left[\frac{1}{2}, 2\right]$ such that $f(x)+xf'(x) > 0$, then the range of the real number $b$ is ______.

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