
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 $f(x)=\ln x-mx^{2}$ and $g(x)= \frac {1}{2}mx^{2}+x (m\in R)$, let $F(x)=f(x)+g(x)$.
1. When $m= \frac {1}{2}$, find the interval where function $f(x)$ is monotonically increasing.
2. If the inequality $F(x)\leqslant mx-1$ always holds true, find the minimum value of the integer $m$.

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