
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
With all angles measured in degrees, consider the product \(\prod_{k=1}^{45} \csc^2(2k-1)^\circ \prod_{k=1}^{45} \sec^2(2k)^\circ = m^n\), where \(m\) and \(n\) are integers greater than 1. Find \(m+n\).

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