
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 $f(x)=-\ln x+x+h$, for any three real numbers $a, b, c$ chosen from the interval $\left[ \frac{1}{e}, e \right]$ such that a triangle with sides of lengths $f(a), f(b), f(c)$ can exist, the range of the real number $h$ is \_\_\_\_\_.

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