
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 chose an acute angle $y$ (strictly between $0$ and $90$ degrees) and calculated $\sin y$, $\cos y$, and $\tan y$. He wrote these values on three different cards, handing them out to Sofia, Liam, and Nina, each receiving one card. After sharing their values, they found that only Sofia could confidently determine her card's associated trigonometric function based solely on the relational size (greater than, less than) of her value compared to others. Identify the trigonometric function on Sofia's card and compute the value for angle $y$ given she is the only one able to deduce her function entirely.

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