
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
The graph of the function $f(x)=\sin(\omega x+\frac{π}{6})(\omega>0)$ is shifted to the left by $\frac{π}{2\omega}$ to obtain the graph of $g(x)$. If the function $g(x)$ is monotonically decreasing on $[0,\frac{π}{2}]$, determine the range of values for $\omega$.

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