
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 $f(x)=x-a\ln x+b$, where $a$ and $b$ are real numbers.
1. If the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is $y=2x+3$, find the values of $a$ and $b$.
2. If $|f′(x)| < \frac {3}{x^{2}}$ holds for $x\in[2,3]$, find the range of values of $a$.

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