
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 function $f(x)=ax+b\ln x$ whose tangent line at the point $(1,a)$ is $y=-x+3$.

1. Find the values of $a$ and $b$.
2. Find the maximum and minimum values of the function $g\left( x \right)=f\left( x \right)-\dfrac{1}{x}$ in the interval $\left[\dfrac{1}{2},2 \right]$.

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