
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
Johan picked an angle $x$ within $(0^\circ, 90^\circ)$ and computed $\sin x$, $\cos x$, and $\tan x$, writing each on separate cards. He gave each card to three students, Alicia, Bettina, and Carla without telling them which function's result they received. After discussing, Bettina was the only one able to determine her card confidently. All three students know each other’s values. Compute the sum of all feasible values for Bettina’s card.

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