
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 picked a different acute angle $y$ (strictly between 0 and 90 degrees) and noted down the values of $\sin y$, $\cos y$, and $\tan y$ on three separate cards. He then distributed these cards to three students, Alex, Betty, and Charles, one card each, and asked them to determine which trigonometric function (sin, cos, or tan) was represented on their card. After sharing the values on their cards among themselves, only Alex was able to definitively identify the trigonometric function of his card. Calculate the sum of all possible values that Joel wrote on Alex's card.

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