
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 now selects an acute angle $x$ (between 0 and 90 degrees) and writes $\sin x$, $\cos x$, and $\tan x$ on three different cards. Each student, Malvina, Paulina, and Georgina, receives one card, but Joel chooses a value $\sin x$ that is a commonly known value, $\sin x = \frac{1}{2}$. The three students know the angle is acute and share the values on their cards without knowing which function produced which. Only Paulina is able to surely identify the function and the specific angle for the value on her card. Determine all possible angles $x$ and find the value that Paulina could identify on her card.

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