
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
Joel selected two different acute angles $x$ and $y$ (both strictly between 0 and 90 degrees) and wrote the values of $\sin x$, $\cos x$, $\tan x$, and $\sec y$ on four different cards. Then he gave those cards to four students, Malvina, Paulina, Georgina, and Bella, one card to each. They shared the values on their cards with each other. Only Bella was able to surely identify which trigonometric function produced the value on her card. Compute the sum of all possible values that Joel wrote on Bella's card.

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