
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 $f(x)=\sin(\omega x+\varphi)$ where $\omega > 0$ is a monotonically decreasing function on the interval $\left(\frac{π}{18},\frac{5π}{36}\right)$, its graph is symmetric about the line $x=-\frac{π}{36}$, and one zero of $f(x)$ is at $x=\frac{7}{72}π$, determine the minimum value of $\omega$.

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