
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 $f(x)=3\sin\left(4x+\frac{\pi}{6}\right)$, stretch the x-coordinates of all points on the graph of $f(x)$ to twice their original length, and then shift it to the right by $\frac{\pi}{6}$ units to obtain the graph of the function $y=g(x)$. Then, determine one of the axes of symmetry of the graph of $y=g(x)$.

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