
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 $f(x)=-2\cos x-x+(x+1)\ln (x+1)$ and $g(x)=k(x^{2}+ \frac {2}{x})$, where $k\neq 0$.

1. Discuss the monotonic intervals of the function $g(x)$.
2. If there exists $x_{1}\in(-1,1]$ such that for any $x_{2}\in( \frac {1}{2},2]$, $f(x_{1})-g(x_{2}) < k-6$ holds, find the range of $k$.

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