
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 maximum value of \(y\) observed in the first positive section of the graph is 3. Find \(a\).

[No actual graph provided, but imagine a similar setup as the original, with possible compression or expansion in the x-axis and shifted vertical asymptotes]

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