
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 $f(x)=a\frac{x+1}{x}+\ln{x}$, the equation of the tangent line at the point (1, f(1)) is y=bx+5.

1. Find the real values of a and b.
2. Find the maximum and minimum values of the function $f(x)$ on the interval $[\frac{1}{e}, e]$, where $e$ is the base of the natural logarithm.

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