
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
Consider the graph of $y = a \cos(bx) + c \sin (dx)$ for constants $a$, $b$, $c$, and $d$. The value of $a$ is known and equals $-3$, $b = 3$, $d = 3$, and the maximum value observed on the graph is $5$. Find $c$.

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