
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 $y = a \sin (bx + c) + d$ for some constants $a,$ $b,$ $c,$ and $d.$ The graph completes five cycles within the interval $0$ to $2\pi$ and has a maximum amplitude above the midline of 4 at $y = 5$ and a minimum amplitude below the midline of -3 at $y = -3$. Find the values of $a$, $b$, $c,$ and $d$ given this new information.

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