
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 an acute angle $x$ (strictly between 0 and 90 degrees) and noted the values of $\sin x$, $\cos x$, and $\tan x$ on three different cards. He then assigned each card to one of three students: Malvina, Paulina, and Georgina, without revealing which trigonometric function was linked to each card. After sharing the values on their cards, only Paulina could certainly determine her trigonometric function. Compute the sum of all possible values that Joel wrote on Paulina's card.

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