
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 wrote $\sin x$, $\tan x$, and $\sec x$ on three different cards. He then distributed these cards to three students: Isabelle, Edgar, and Sam, one card to each. After sharing the values on their cards with each other, only Isabelle could accurately identify which function produced the value on her card. Compute the sum of all possible values that Joel wrote on Isabelle's card.

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