
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
Elective 4-5: Special Topics on Inequalities  
Given the inequality $x^2 + px + 1 > 2x + p$.  
(1) If the inequality always holds when $|p| \leq 2$, find the range of $x$.  
(2) If the inequality always holds when $2 \leq x \leq 4$, find the range of $p$.

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