
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 that the maximum value of \(y\) when positive is 3, and period of the function is \(2\pi\). Find \(a\).

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