
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 functions $f(x)=x-a\ln x$ and $g(x)=- \frac {1+a}{x}$, where $a\in\mathbb{R}$,

1. Find the monotonic intervals of the function $h(x)=f(x)-g(x)$ when $a > 0$.
2. If there exists a point $x_{0}$ in $[1,e]$ such that $f(x_{0}) < g(x_{0})$, find the range of $a$.

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