
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 chooses an angle $y$ strictly between 0 and 180 degrees and writes the values of $\sin y$, $\cos y$, and $\tan y$ on three different cards. He gives each card to one of three students: Alice, Bob, and Carol. They share the values on their cards but only Alice is able to definitively determine which trigonometric function produced the value on her card. Compute the sum of all possible values that Joel wrote on Alice's card, assuming $y$ is in the range $(90^\circ, 180^\circ)$.

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