
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
Let \( f(x) = x^2 + mx + n \). If the inequality \( |f(x)| > 2 \) has no solution on the interval \([1, 5]\):
1. Find the value of \( f(1) - 2f(3) + f(5) \).
2. Find all real pairs \((m, n)\).

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