
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 \( g(x) = x^4 + 20x^3 + 98x^2 + 100x + 25 \). Let \( w_1, w_2, w_3, w_4 \) be the four roots of \( g \). Find the smallest possible value of \( |w_a w_b + w_c w_d| \) where \( \{a, b, c, d\} = \{1, 2, 3, 4\} \).

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