
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 the constants $a > 0,$ $b > 0,$ and $c \neq 0$. The graph reaches a maximum value of 3 and a minimum value of -3, with a period of $4\pi$. The graph of $y$ crosses the x-axis at $x=\frac{\pi}{2}$. Find the values of $a$, $b$, and $c$.

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