
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
For all real numbers \( p \) that satisfy \( p = 4 \sin^4 \alpha \) where \( \alpha \in \left[ \frac{\pi}{6}, \frac{5\pi}{6} \right] \), and the inequality \( x^2 + px + 1 > 2x + p \) holds for all \( x \), determine the range of values for \( x \).

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