
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 $f(x)=2\sin(\omega x+\varphi)$ where $(\omega>0, -\frac{π}{2}<\varphi<\frac{π}{2})$, the distance between two adjacent symmetric axes of the graph is $\frac{π}{6}$, and it is symmetric about the point $(\frac{5π}{18},0)$. Determine the value of $\varphi$.

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