
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 point $P(t, 1)$ on the graph of the function $y = \sin 2x$ is translated $S (S > 0)$ units to the right to obtain the point $P'$ on the graph of the function $y = \sin (2x - \frac{\pi}{3})$, determine the value of $t$ and the minimum value of $S$.

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