
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 that $O$ is the coordinate origin, $\overrightarrow{OA}=(2\cos x, \sqrt {3})$, $\overrightarrow{OB}=(\sin x+ \sqrt {3}\cos x,-1)$, and $f(x)= \overrightarrow{OA} \cdot \overrightarrow{OB}+2$.

1. Find the equation of the axis of symmetry for the function $f(x)$.
2. When $x \in (0, \frac{\pi}{2})$, if the function $g(x)=f(x)+m$ has zero points, find the range of $m$.

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