
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
Alice picked an angle $x$ (strictly between 90 and 180 degrees) and calculated the values of $\sin x$, $\cos x$, and $\sec x$. She wrote these values on three separate cards. Ella, Betty, and Nancy received one card each from Alice. After sharing the values, only Ella was able to certainly identify which function Alice had used for her card. Calculate the sum of all possible values that could be on Ella's card.

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