
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 \( y = a \cos bx \) for some constants \( a > 0 \) and \( b > 0 \). The graph has its maximum value of 3 at \( x = 0 \) and the first zero occurs at \( x = \frac{\pi}{6} \). Find the values of \( a \) and \( b \).

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