
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) = ln(x) - $\frac {1}{x}$ - mx, which is an increasing function in the interval (0, 1), where m is a real number.

1. Find the range of m.
2. When m takes the maximum value, if the line l: y = ax + b is the tangent line of the function F(x) = f(x) + 2x, and a, b are real numbers, find the minimum value of a + b.

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