
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
Below is the graph of \( y = a \sin(bx + c) \) for some constants \( a > 0 \), \( b > 0 \), and \( c \). The graph reaches its maximum value at \( 3 \) and completes one full cycle by \( 2\pi \). There is a phase shift where the maximum first occurs at \( \pi/6 \). Find the values of \( a \), \( b \), and \( c \).

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