
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 function $f(x)=2 \sqrt {3}\sin (3ωx+ \dfrac {π}{3})$ where $ω > 0$,

(1) If $f(x+θ)$ is an even function with a period of $2π$, find the values of $ω$ and $θ$.
(2) If $f(x)$ is an increasing function on $(0, \dfrac {π}{3})$, find the maximum value of $ω$.

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