
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 $y = a \sec bx$ for some positive constants $a$ and $b.$ The graph shows the function having vertical asymptotes at $x = \pm \frac{\pi}{2}, \pm \frac{3\pi}{2}$, and a maximum amplitude of 3 on the positive side. Find the value of $a$.

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