
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) = $\frac{a}{x}$ + lnx,
(1) If one tangent line of f(x) is y = -x + 3, find the monotonic intervals of f(x);
(2) Suppose the function g(x) = f(x) - 1 has two zeros on the interval [e^(-1), e], find the range of the real number a.

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