
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 $y=\sin \left( x-\frac{\pi }{6} \right)$ is translated to the right by $\frac{\pi }{4}$ units, and then the horizontal coordinates of all points on the graph are doubled (the vertical coordinates remain unchanged). Determine the analytical expression of the resulting graph.

A) $y=\sin \left( 2x-\frac{5\pi }{12} \right)$
B) $y=\sin \left( \frac{x}{2}-\frac{5\pi }{12} \right)$
C) $y=\sin \left( \frac{x}{2}+\frac{\pi }{12} \right)$
D) $y=\sin \left( \frac{x}{2}-\frac{5\pi }{24} \right)$

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