
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 $f(x)=\sin (ωx+φ)$, where $ω > 0,|φ| < \dfrac {π}{2},x∈R$, the distance between two adjacent symmetry axes is $\dfrac {π}{2}$, and $f( \dfrac {π}{6})$ is the maximum value. Determine the intervals where the function $f(x)$ is monotonically increasing in the interval $[0,π]$.

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