
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 function $y=\sin \left( 6x+\frac{\pi }{4} \right)$ is transformed such that the vertical coordinates remain unchanged, while the horizontal coordinates are stretched to three times their original length and then shifted to the right by $\frac{\pi }{8}$ units. Determine one of the symmetry centers of the resulting function.

A) $\left( \frac{\pi }{2},0 \right)$
B) $\left( \frac{\pi }{4},0 \right)$
C) $\left( \frac{\pi }{9},0 \right)$
D) $\left( \frac{\pi }{16},0 \right)$

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