
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
Suppose $\sec x + \tan x = \frac{19}{6}$ and $\csc x + \cot x = \frac{m}{n},$ where $\frac{m}{n}$ is in lowest terms. Find $m+n.$

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