
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) = 2sinωx(cosωx + $\sqrt{3}$sinωx) - $\sqrt{3}$ (ω > 0) has a minimum positive period of π.
(1) Find the interval where the function f(x) is monotonically increasing.
(2) If the graph of function f(x) is shifted to the left by $\frac{\pi}{6}$ units and up by 2 units to obtain the graph of function g(x), find the sum of the zeros of function g(x) in the interval [0, 5π].

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