
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 the function $f(x)= \sqrt {3}sinωxcosωx+cos^{2}ωx$ has a symmetry center and its adjacent symmetry axis have a distance of $\frac {π}{4}$.
(1) Find the equation of the symmetry axis and the interval where the function is monotonically increasing;
(2) After shifting the graph of the function $y=f(x)$ to the right by $\frac {π}{6}$ units, then compressing the x-coordinates of all points on the resulting graph to $\frac {1}{2}$ of their original length (y-coordinates remain unchanged) to obtain the graph of $y=g(x)$, find the range of $g(x)$ when $x\in($$- \frac {π}{12}$, $\frac {π}{3}$).

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