
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 that \\(x=1\\) is an extremum point of \\(f(x)=2x+ \dfrac{b}{x}+\ln x\\).

\\((1)\\) Find the interval of decrease for the function \\(f(x)\\);

\\((2)\\) Let the function \\(g(x)=f(x)- \dfrac{3+a}{x}\\), if the function \\(g(x)\\) is increasing in the interval \\([1,2]\\), find the range of the real number \\(a\\).

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