
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 $y=\sin \left( \frac{1}{2}x-\frac{\pi }{3} \right)$, translate the graph $\frac{\pi }{2}$ units to the right, then shrink the x-coordinates of all points on the obtained graph to $\frac{1}{2}$ of their original length (y-coordinates remain unchanged). Determine a monotonically increasing interval for the resulting graph's corresponding function.

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