
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
Jonas selected an angle $x$ strictly between 30 and 120 degrees and wrote the values of $\sin x$, $\cos x$, $\tan x$, and $\sec x$ on four different cards. He then gave those cards to four students: Matilda, Philippa, Gordon, and Cynthia, one card to each. After sharing their values with each other, only Matilda was certain which trigonometric function produced the value on her card. Compute the sum of all possible values that Jonas wrote on Matilda's card.

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